How do I make a div full screen?

CSS way:

#foo {
   position: absolute;
   top: 0;
   right: 0;
   bottom: 0;
   left: 0;
}

JS way:

$(function() {
    function abso() {
        $('#foo').css({
            position: 'absolute',
            width: $(window).width(),
            height: $(window).height()
        });
    }

    $(window).resize(function() {
        abso();         
    });

    abso();
});

You can use HTML5 Fullscreen API for this (which is the most suitable way i think).

The fullscreen has to be triggered via a user event (click, keypress) otherwise it won't work.

Here is a button which makes the div fullscreen on click. And in fullscreen mode, the button click will exit fullscreen mode.

$('#toggle_fullscreen').on('click', function(){
  // if already full screen; exit
  // else go fullscreen
  if (
    document.fullscreenElement ||
    document.webkitFullscreenElement ||
    document.mozFullScreenElement ||
    document.msFullscreenElement
  ) {
    if (document.exitFullscreen) {
      document.exitFullscreen();
    } else if (document.mozCancelFullScreen) {
      document.mozCancelFullScreen();
    } else if (document.webkitExitFullscreen) {
      document.webkitExitFullscreen();
    } else if (document.msExitFullscreen) {
      document.msExitFullscreen();
    }
  } else {
    element = $('#container').get(0);
    if (element.requestFullscreen) {
      element.requestFullscreen();
    } else if (element.mozRequestFullScreen) {
      element.mozRequestFullScreen();
    } else if (element.webkitRequestFullscreen) {
      element.webkitRequestFullscreen(Element.ALLOW_KEYBOARD_INPUT);
    } else if (element.msRequestFullscreen) {
      element.msRequestFullscreen();
    }
  }
});
#container{
  border:1px solid red;
  border-radius: .5em;
  padding:10px;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div id="container">
  <p>
    <a href="#" id="toggle_fullscreen">Toggle Fullscreen</a>
  </p>
  I will be fullscreen, yay!
</div>

Please also note that Fullscreen API for Chrome does not work in non-secure pages. See https://sites.google.com/a/chromium.org/dev/Home/chromium-security/deprecating-powerful-features-on-insecure-origins for more details.

Another thing to note is the :fullscreen CSS selector. You can append this to any css selector so the that the rules will be applied when that element is fullscreen:

#container:-webkit-full-screen,
#container:-moz-full-screen,
#container:-ms-fullscreen,
#container:fullscreen {
    width: 100vw;
    height: 100vh;
    }

When you say "full-screen", do you mean like full-screen for the computer, or for taking up the entire space in the browser?

You can't force the user into full-screen F11; however, you can make your div full screen by using the following CSS

div {width: 100%; height: 100%;}

This will of course assume your div is child of the <body> tag. Otherwise, you'd need to add the following in addition to the above code.

div {position: absolute; top: 0; left: 0;}