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JavaScript: how to pass additional information to source page?

I have a website and when a user follows an internal link I would like to pass some extra information to a new page, so JavaScript on the destination page could do some useful highlighting.
There is an option to pass that information via the link parameters (GET), but it will generate lots of virtually duplicate pages and break pretty URLs concept. Another way is to make a webapp using AJAX, but it will also bound content to a single URL.
How can I transparently pass some information to the new page during navigation w/o messing with site's URL structure?

You could store the data in local storage or session storage, and retrieve it again on the destination page.

So you have a few options.
Form Submission
First option post a form with the data. Add a hidden form, on the anchor click capture the click event, set the hidden fields with the values you want to send to the next page, and submit the form. On the next page, read the post parameters in the backend and update the page.
Local Storage
On click of the anchor, set localStorage to the values you want to appear on the next page. When the next page loads, read the localStorage values and update the page. Note: The server will not have access to the values
Ajax with pushState
Use Ajax to submit the form. When the Ajax call returns, use window.history.pushState to update the url with whatever url you want to be displayed to the user.

One of the options not mentioned is to create a dirty URL:
/destination/param1/value1/...
then strip additional parameters at server-side and redirect:
/destination
keeping additional values stored at server-side (e.g. via sessions). I still prefer using sessionStorage in a real application, but it worth mentioning anyway.

What do you mean it will "bind content to a single url"? AJAX request is the first thing that comes to my mind as the solution to this problem. You dont have to use the url of the page to make the ajax request, you can build the url inside your javascript based on whatever conditions exist in your application.
Besides AJAX and passing parameters in the URL, the only other thing I can think of is to use Cookies. That of course runs into problems if the user has cookies disabled. I think an Ajax call to your server is the most robust way of handling the problem.

Is it possible to get data from redirection page in AJAX?

I'm in trouble. I'm trying to do something which can appear easy but I don't manage to do it.
Here is the situation :
I have 3 different html pages :
The first one called index.html is my main page with a button to lauch a test in AJAX (I'm gonna talk about it after).
The second one corresponds to a redirection to the third page.
The third one has data.
What I wanna do is :
Click on "test" button on the first page and then start an AJAX request on the second one to reach data from the third one (with the redirection) to print it in the first.
I mean the first page calls the second one in AJAX, but the just to redirect on a specific third page. Depending on the third page which is called, data returned to the first page will change.
Do you think it's possible to find a solution to this problem in Javascript ? I hope I have been clear enough.
Thank you in advance for answer.

What you are describing doesn't really make sense. There are methods of redirection that AJAX follows (an HTTP 301 code, for example). However, what you are describing is not that sort of redirect. You are describing Javascript code that, when run, will redirect the browser elsewhere.
However, you are not loading that Javascript with the browser, you are downloading the page via AJAX. Once it is downloaded, you will have the text that represents that page, but in order to find out where it would redirect to when run, you would either have to run it and somehow capture the redirect value (not recommended), or parse it yourself (also not recommended).
There are other options that could work, depending on what you are trying to accomplish:
The server could return an HTTP redirect code when the second page is requested
The second page could instead be a text or JSON file containing a URL, which the first page could read, then request data from that URL.
If there is logic in the second page that determines where the redirect goes, it could be moved to the first page
You could have the second page employ server-side scripting (PHP, etc) to determine what data should be returned and return it directly to the first page

How do you make a link perform an action without reloading a page?

The clearest example of this I could think of is the Reddit Upvote/downvote buttons how when you click the button, the value for upvotes is updated, the upvote button lights up, and the page DOES NOT reload, you just stay exactly where you are on the page.
I am trying to make a feature similar to this and I can totally figure out how to do it with reloading, but I want it to not reload so the user experience isn't disrupted.
Is it possible to do this with php? or would I need to use javascript or something?
The action I would need it to perform would be a basic update query in the database.

This would be done with an Ajax call to your php script. Ajax is designed for these asynchronous updates and/or reloads.
Another way you can do this is with HTML5 WebSockets. You could have the client send a trigger to the server when the user clicks the upvote, and then the server could update and push back the data. It would, however, be a bit overfill for this.

If what you want to do is to contact a server to either send it some state or to retrieve some state from the server (or both), then you would use AJAX with javascript in order to contact the server without reloading the page. You can then also use javascript to update the state of your page after the operation. That is generally what the Reddit page you refer to is doing.
Conceptually, you'd set up your page like this:
Put the link on the page.
With javascript install an event handler so you are notified of a click on the link.
When the link is clicked, your event handler will be called.
Prevent the default behavior of the link so the browser doesn't navigate to a new page.
Then, in the event handler, send your data to the server using AJAX. You will obviously need a URL on your server and server process that can accept and process the data for you and return a value if you need to.
If you need the response from the server, then set up a callback function for when the AJAX call completes (this will be some indeterminate time in the future).
Then, if you need to change the current page in any way (like show one more upvote), then you can modify the current page with javascript to show that new state.
Ajax is easier to use with a library (like jQuery) that contains some ajax support code, but you can certainly implement it in plain javascript too.
Here's one example of ajax with plain javscript. You can find many other examples with Google.
This MDN tutorial on AJAX seems pretty helpful too to show you how it works.

You could use JavaScript to do this. Here's a quick sample:
Vote Up
Simple solution in JavaScript:
var el = document.getElementById("upvoteBtn");
el.addEventListener("click", onVoteClick);
function onVoteClick(e) {
e.preventDefault();
// do something
}
Here's a fiddle.
NOTE: I see you'd be updating the database. In that case, you would have to use AJAX in the onVoteClick function (or use XMLHttpRequest) for this. JavaScript is a client-side programming language and will not be able to communicate to the server without the use of AJAX or XMLHttpRequest. Using the jQuery library, you should be able to write AJAX pretty easy.

It's called AJAX.
With AJAX you can send a request in the background.
The easiest way is to use the jquery libary for this.
You can also output some data as JSON back to the script if you want to take some other actions depending on the result from that query.
A good tutorial is this one.
It also explains how this requests (called: XMLHttpRequest) work.

You need to use Javascript's XMLHttpRequest

You can use AJAX...
It allows you to use JavaScript (client side) to call server side functions. Here's a good example.

Call JS function before redirect

The situation is as follows:
A user on the client side enters some data and presses a command button that initiates an ajax request. Depending on the input data the JSF Bean on the server side redirects to different pages. But in addition the HTML5 features localstorage respectively sessionstorage should be updated on client side, also depending on the results from the bean. For the storage some data entered from the user is necessary, so that the java script for the storage has to be within the original page.
Now, the problem seems to be that after the response the redirect is always done first, before executing the js function and so it is not possible to access the input data from the user on the client side of curse.
I tried things for calling the js function after pressing the command button like "oncomplete" on the client side using callback parameters (redirect takes place earlier) or RequestContext.execute from the server side (but this internally also uses the oncomplete event i think).
One possible solution I could imagine is to use window.onunload on client side and a hidden input formular to get the result of the bean. But isn't there a better solution?

You need to redirect by JS instead of by JSF. Return null from action method so that it returns to the same page and then execute the following script to perform a redirect in JS.
window.location = newURL;

If you use PrimeFaces with JSF then it's possible to make global override of PrimeFaces.ajax.ResponseProcessor.doRedirect in javascript to put any custom code before actual redirect happens:
PrimeFaces.ajax.ResponseProcessor.doRedirect = function(node) {
// <<<< your code is here >>>>
window.location = node.getAttribute('url');
}
Put this code in some js file and include it in all your pages.

Is there any way to call JavaScript function from a perl script?

I am trying to write a Perl script that will take a user parameter from command line and with his parameter, Perl script will call a JavaScript function in a HTML page. How can I go ahead to with this?

Not that I've seen. Perl is strictly server side, and JS functions you're talking about are on the client.
The closest you would get is have the Perl script write a block into the HTML page so that the page fires it on load to perform the action. But that's a little shaky at best to do.

It depends on whether the browser or server will be taking the first step.
If the server needs to run code first and then execute some JS, then #skyburner's solution would work. Essentially you would already have some functions defined on the page, but then you would dynamically add a block of JS to call whichever function you need to.
However, if the Perl is being run due to a user's action on the current page (such as clicking something or submitting a form), then AJAX would be the way to go. You would use JS to submit an HTTP request to the Perl script. The Perl would then return some value back to the JavaScript and execute some function based on this result. This would all happen "behind-the-scenes" without the user leaving the page.

If I understand correctly about what you want, since not all the browsers support socket, this is what you can do:
Have an ajax service call periodically sending requests to the server for update
Once the the parameters from the command line are taken, you can send the result along with an ajax response back to the page, and call the function in the ajax request callback function.
Also, another option, you can use reverse ajax to accomplish this. See Wikipedia about reverse ajax (comet), especially Ajax with long polling.