We Keep Coding

How can I hide my div using jQuery, and then showing it again by pressing a different div?

What I want to do is:
Make my div hidden when the page loads, and then when you click a different div it will show. My limited knowledge doesn't really allow me to make this happen. What am I doing wrong?
jQuery:
$(document).ready(function(){
$('#trojkat2').click(function(){
$('#login').hide();
});
});
</script>
"trojkat2" is the div I want to click to make "login" appear.
HTML:
<div class="kwadrat2">
<div class="trojkat2">
<div class="trojkat_bg2"></div>
</div>
</div>
<div class="login">
<img style="height: 550px; width: 280px; border-radius: 10px;" src="buymenu.jpg">
</div>
What have I done wrong?

First, hide your #login div when document ready by .hide() function, after click $(.trojkat2), use show() to make #login appear, by the way class selector is . instead of #
$(document).ready(function(){
$('.login').hide();
$('.trojkat2').click(function(){
$('.login').show();
});
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div class="kwadrat2">
<div class="trojkat2">click here
<div class="trojkat_bg2"></div>
</div>
</div>
<div class="login">
<img style="height: 550px; width: 280px; border-radius: 10px;" src="buymenu.jpg">
</div>

Try this:
$('.trojkat2').click(function() {
$('.login').show();
});

Your example doesn't have an element with id = trojkat2 so your selector $("#trojkat2") won't work. Same is for #login. Instead you need to change it to a class selector :
$('.trojkat2').click(function(){
$('.login').hide();
});
Example : http://jsfiddle.net/DinoMyte/nrNX8/529/

In your HTML code, you created classes called login and trojkat2. However, in your jQuery, you are telling it to call the IDs called login and trojkat2. Classes are preceded with a "." and IDs are preceded with a "#". Instead, try the following code in your jQuery:
$(document).ready(function(){
$('.trojkat2').click(function(){
$('.login').hide();
});
});

Make an image visible when I hover over another

Essentially I have an interactive map which contains 4 div statements each of which contains an image of an island. I would like to create an on hover event which will display a corresponding sailing timetable depending on which image the user hovers. e.g. island 1 should display timetable 1.
I have the following code so far and ideally I am looking for a javascript or css solution:
<div class="Map">
<div id="Island_Morar">
<img src="images/IsleOfMorar.jpg"/>
</div>
<div id="Island_Rum">
<img src="images/IsleOfRum.jpg"/>
</div>
<div id="Island_Eigg">
<img src="images/IsleOfEigg.jpg"/>
</div>
<div id="Island_Muck">
<img src="images/IsleOfMuck.jpg"/>
</div>
</div>
<img id="TimetableEigg" src="images/TimetableEigg.jpg">
any help is appreciated.

You need some different markup if you want a plain css solution. If you want to have different timetables for each hover you should go with something like this:
markup
<div class="tt-container" id="Island_Rum">
<img src="images/IsleOfRum.jpg"/>
<img class="timetable" src="images/TimetableRum.jpg">
</div>
<div class="tt-container" id="Island_Eigg">
<img src="images/IsleOfEigg.jpg"/>
<img class="timetable" src="images/TimetableEigg.jpg">
</div>
<div class="tt-container" id="Island_Muck">
<img src="images/IsleOfMuck.jpg"/>
<img class="timetable" src="images/TimetableMuck.jpg">
</div>
</div>
css
.timetable {
display : none;
}
.tt-container:hover .timetable {
display : block;
}
That should do the trick

If you want to keep your current HTML code, I'd make three image blocks for timetables, and initially set them all to display: none; and add onmouseover event handlers to island elements which would contain Javascript statement which will set disply: block; on appropriate timetable.
Something like this:
<div class="Map">
<div id="Island_Morar" onmouseover="document.getElementById('TimetableEigg1').style.display = 'block';">
<img src="images/IsleOfMorar.jpg"/>
</div>
<div id="Island_Rum" onmouseover="document.getElementById('TimetableEigg2').style.display = 'block';" >
<img src="images/IsleOfRum.jpg"/>
</div>
<div id="Island_Eigg" onmouseover="document.getElementById('TimetableEigg3').style.display = 'block';" >
<img src="images/IsleOfEigg.jpg"/>
</div>
<div id="Island_Muck" onmouseover="document.getElementById('TimetableEigg4').style.display = 'block';" >
<img src="images/IsleOfMuck.jpg"/>
</div>
</div>
<img id="TimetableEigg1" src="images/TimetableEigg1.jpg">
<img id="TimetableEigg2" src="images/TimetableEigg2.jpg">
<img id="TimetableEigg3" src="images/TimetableEigg3.jpg">
<img id="TimetableEigg4" src="images/TimetableEigg4.jpg">

Seems you barely know the basics of HTML and already trying to jump too deep. External libraries will help you and speed up your progress. I see people gave you CSS solutions so here is a JS solution.
First thing is download the well known JS library called jQuery.
then load this file to your page and add a script at the bottom of your body tag:
$("div.map").on("mouseover", "#Island_Morar", function(e) {
$(this).show(); // option one
//$(this).addClass("class-name"); // option two
}).on("mouseout", "#Island_Morar", function(e) {
$(this).hide(); // option one
//$(this).removeClass("class-name"); // option two
});
With this script you can do whatever you want, for example - use the second option of adding and removing classes in order to animate your Timetables (see Example).

Possible CSS / JQuery solution:
$(".Map a").hover(
function() {
$('#' + $(this).attr('class')).show();
}, function() {
$('#' + $(this).attr('class')).hide();
}
);
.timetables img { display:none; }
<div class="Map">
<a href="#" class="islandmorar">
<img src="images/IsleOfMorar.jpg"/>
</a>
<a class="islandrum">
<img src="images/IsleOfRum.jpg"/>
</a>
<a class="islandeigg">
<img src="images/IsleOfEigg.jpg"/>
</a>
<a class="islandmuck">
<img src="images/IsleOfMuck.jpg"/>
</a>
</div>
<div class="timetables">
<img id="islandmorar" src="images/TimetableEigg.jpg"/>
<img id="islandrum" src="images/TimetableEigg.jpg"/>
<img id="islandeigg" src="images/TimetableEigg.jpg"/>
<img id="islandmuck" src="images/TimetableEigg.jpg"/>
</div>

Pure CSS solution but you need to place the large image in .main div
the first image will be displayed first and will change on hover on other images and when you leave move out of the main div it will show the first image
Note: used random images
.Map > div {
display: inline-block;
}
img.two,
img.three,
img.four,
#Island_Rum:hover ~ img.one,
#Island_Muck:hover ~ img.one,
#Island_Eigg:hover ~ img.one {
display: none;
}
img.one {
display: block;
}
#Island_Morar:hover ~ img.one {
display: block;
}
#Island_Rum:hover ~ img.two {
display: block;
}
#Island_Eigg:hover ~ img.three {
display: block;
}
#Island_Muck:hover ~ img.four {
display: block;
}
<div class="Map">
<div id="Island_Morar">
<img src="http://placeimg.com/100/100/any/animals" />
</div>
<div id="Island_Rum">
<img src="http://placeimg.com/100/100/any/arch" />
</div>
<div id="Island_Eigg">
<img src="http://placeimg.com/100/100/any/nature" />
</div>
<div id="Island_Muck">
<img src="http://placeimg.com/100/100/any/tech" />
</div>
<img class="one" src="http://placeimg.com/400/400/any/animals" />
<img class="two" src="http://placeimg.com/400/400/any/arch" />
<img class="three" src="http://placeimg.com/400/400/any/nature" />
<img class="four" src="http://placeimg.com/400/400/any/tech" />
</div>

Don't put class="map" to the wrapper div, give it to every div with id beginning with "Island_...".
Do the same with your timeTable images, give them a class "timeTable".
Put this before your "head" end tag :
<script>
"use strict";
//wait for every element to be loaded
window.onload = function(){initialization();}
</script>
Then, put this before your "body" end tag :
<script>
"use strict";
//first create a function that hides elements with class 'timeTable'
function hide(elements){
var htmlClass = document.getElementsByClassName(elements);
//hide every element with class
for (var i = 0 ; i < htmlClass.length ; i++){
htmlClass[i].style.display = "none";
htmlClass[i].style.visibility = "hidden";
}
}
//create a function that show only the timeTable you want
function show(element){
document.getElementById(element).style.display = "block";
document.getElementById(element).style.visibility = "visible";
}
function initialization(){
//replace 'someMapId' with the id of the image you are hovering
//replace 'someTimeTableId' with the id of the image you want to show
//replace 'timeTable' with the name of a class you want to hide
document.getElementById("someMapId").onmouseover = function(){
hide("timeTable");
show("someTimeTableId");
}
//repeat these 3 lines for every image the user will hover
}
</script>
Don't forget the quotes when using the functions.
You should use css for styling and javascript for interactions.
You don't need jQuery for basic scripts like that, it only slows page loading and keeps you away from learning basic javascript.
(Ok, I edited mistakes, now it works ;)
jsFiddle

jQuery Show/Hide - Make other elements have a smoother transition

Is there a way for the label/form below the 'myContent' div to have a smoother transition when I am hiding/showing it?
Currently, when the myContent div is toggled, the other elements below it 'jump' into place - it would be great if I could figure out a way to slide them up into their correct location. What do you think?
JavaScript
function toggleDiv(divId) {
jQuery("#" + divId).toggle("slide", {
direction: "up"
});
}
function ShowThing(divID) {
jQuery("#" + divID).show("slide", {
direction: "up"
}, 500);
}
function HideThing(divID) {
jQuery("#" + divID).hide("slide", {
direction: "up"
}, 500);
}
HTML
Toggle Button
<button onclick="ShowThing('myContent');">Show</button>
<button onclick="HideThing('myContent');">Hide</button>
<div>
<div id="myContent" style="background-color: #aaa; padding: 5px 10px;">The content in this div will hide and show (toggle) when the toggle is pressed.
</div>
</div>
<div>
<label for="cool-field">Name</label>
<input type="text" name="cool-field" id="cool-field" />
</div>

Click Here for jsFiddle
Optimized the javascript so that all code is based on jQuery.
HTML code
Toggle Button
<button id="showthing">Show</button>
<button id="hidething">Hide</button>
<div>
<div id="myContent" style="background-color: #aaa; padding: 5px 10px;">The content in this div will hide and show (toggle) when the toggle is pressed.
</div>
</div>
<div>
<label for="cool-field">Name</label>
<input type="text" name="cool-field" id="cool-field" />
</div>
jQuery Code:
$(function(){
$('a.togglebtn').click(function(){
$('#myContent').stop().slideToggle(500);
return false;
});
$('#showthing').click(function(){
$('#myContent').slideDown(500);
});
$('#hidething').click(function(){
$('#myContent').stop().slideUp(500);
});
});

Your Jsfiddle is blank.
Instead of show() you can use slideDown('slow');
for hide you can use slideUp('slow'); Also you can set direction.
Otherwise you can use JQuery Animate

onMouseOut Event is not working in my HTML

I have this code in my page.
<div class="MenuItemContainer">
<a href="javascript:ShowHelpMenu()">
<div class="MenuItemContent">
<div>
<img src="/Content/TopMenu/Icons/Help.png" alt="Help" />
</div>
<div>
Help
</div>
<div id="divHelpMenu" class="HelpMenuDisplayDiv" style="z-index:9999; width: 400px;margin: 10px 20px; background-color:Aqua" onmouseout="HideHelpMenu()">
<%=Session["helpUrls"]%>
<%-- <%=Session["Links"]%>
--%>
</div>
</div>
This is my Functions
function ShowHelpMenu() {
$("#divHelpMenu").css("display","block");
}
function HideHelpMenu() {
$("#divHelpMenu").css("display","none");
}
When I click on Help Link I can display all the Links but when I mouseover on the links my Div tag is closing. onmouseout event is not firing when I mouse out from the div tag.
its closing when I mouse in on HTML links.
Thanks

It looks like you have your mouse out code on the wrong element, I think you'd want it on the MenuItemContainer div. You could also remove your inline mouse out code and bind the event to the correct container when you show the help div, like this:
function ShowHelpMenu() {
$("#divHelpMenu").css("display","block");
$('#MenuItemContainer').bind('mouseout.helpmenu', HideHelpMenu);
}
function HideHelpMenu() {
$("#divHelpMenu").css("display","none");
$('#MenuItemContainer').unbind('mouseout.helpmenu');
}

You missing some closing tags. Try next HTML markup:
<div class="MenuItemContainer">
<a href="#" onclick="javascript:ShowHelpMenu();return false;">
<div class="MenuItemContent">
<div><img src="/Content/TopMenu/Icons/Help.png" alt="Help" /></div>
<div>Help</div>
</div>
</a><br/>
<div id="divHelpMenu" class="HelpMenuDisplayDiv"
style="display:none;z-index:9999; width: 400px;margin: 10px 20px; background-color:Aqua"
onmouseout="HideHelpMenu()">
Link1<br/>
Link2<br/>
Link3<br/>
Link4<br/>
Link5<br/>
Link6<br/>
</div>
</div>

I got it working,
$(document).ready(function () {
$('#divHelpMenu').hover(function () {
$("#divHelpMenu").css("display", "block");
}, function () {
$("#divHelpMenu").css("display", "none");
});
});

Fading one div into another

I'm having some slight problems with fading one div into another, here's my code (and test page):
HTML:
<div id="grid">
<div class="grid-box">
<div class="phase-1">
<img class="grid-image" src="http://teamworksdesign.com/v2/wp-content/themes/default/images/dtr.jpg" alt="" height="152" width="210" />
<div class="grid-heading">
<h2>DTR Medical</h2>
<h3>Branding, Web, Print</h3>
</div>
</div>
<div class="phase-2">
<div class="grid-info">
<h4>Probeything 2000</h4>
<p>Marketing unglamorous single-use medical intruments is not simple. We helped Neurosign increasetheir sales by 25% and increasemarket awareness.</p>
</div>
<div class="grid-heading-hover">
<h2>DTR Medical</h2>
<h3>Branding, Web, Print</h3>
</div>
</div>
</div>
</div>
Javascript:
<script type="text/javascript">
$(document).ready(function(){
$(".phase-2").hide();
});
$(function(){
$('.grid-box').hover(
function(){
$('.grid-box .phase-1').fadeOut(200, function(){
$('.grid-box .phase-2').fadeIn(200);
});
},
function(){
$('.grid-box .phase-2').fadeOut(200, function(){
$('.grid-box .phase-1').fadeIn(200);
});
}
);
});
</script>
CSS:
.phase-1 .grid-image {
width:210px;
height:220px;
overflow:hidden;
}
.phase-2 {
position:relative;
top:-220px;
}
UPDATE:
I have one "working" (see test link in question). Is it possible to stop it fading to white then fading in the next phase? I want to fade the two div into each other rather than to white first.

If you type $ on the console, it answer undefined, so it probably was redefined by some other script. To use $ meaning jQuery again, use the following syntax
$(document).ready(function($) {
// $ means jQuery again in here
});
Notice the $ as the first argument of the function call.
Documentation here.