Generally, any decently sized web project will use about five languages: HTML, CSS, Javascript, some kind of server-side “getting things done” language (ASP, JSP, CGI scripts with Perl, PHP, etc.), and some variant of SQL for database connectivity.
(This is, of course, hand-waving away the argument about whether or not HTML and CSS count as programming languages – I’m the “they are, but just not Turing-complete languages” camp, but that’s a whole other thread.)
Some examples of how all those work together:
If you’re going the best-practices route, the structure of a web page is in HTML, and the instructions for how to display it are in CSS – which could be in the same file, but don’t have to be. The CSS contains a bunch of classes, which the HTML refers to, and it’s up to the browser to figure out how to click them together.
Taking all that a step further, any javascript scripts on that page can alter any of the HTML/CSS that is present (change contents of HTML entities, swap out one CSS class for another, change the behavior of the CSS, and so on.) It does this via something called the Document Object Model, which is essentially a language and platform-independent API to manipulate HTML pages in an object-like manner (at which point I’ll back away slowly and just provide a link to the relevant wiki article.)
But then, where does all the HTML / CSS / Javascript come from? That’s what the server-side language does. In the simplest form, the serer-side language is a program that returns a giant string holding an HTML page as its output. This, obviously, can get much more complex: HTML forms and query string parameters can be used as input for our server side program, and then you have the whole AJAX thing where the javascript gets to send data directly to the server language as well. You can also get fancy where the server language can customize the HTML, CSS, and Javascript that gets spit out – essentially, you have a program in one language writing a program in another language.
The Server-side language to SQL connection works much the same. There are a lot of ways to make it both more complex and safer, but the simplest way is for your server language to dynamically build a string with a SQL command in it, hand that to the database via some kind of connector, and get back a result set. (This is a case where you really do have a function that boils down to someValue = database.executeThisSQLCommand( SQLString ). )
So to wrap this up, different languages in this case either communicate by actually writing programs in each other, or by handing data around in very simple easy to parse formats that everybody can understand. (Strings, mainly.)