I'm not sure if this is a coding question or not(?).
Installing a jQuery package will usually provide completions for jQuery methods and/or syntax highlighting. If installed you normally might select jQuery by clicking the syntax list at the bottom-right corner of your screen. However, this will usually work with separate .js files, not necessarily with code embedded in an HTML file.
If it's a coding question then you might be better off placing your scroll() event inside the document.ready method. And you need to include the jQuery library firstly:
// The social div
$homeDiv = $('.home');
//Get scroll position of window
var windowScroll = $(this).scrollTop();
'opacity' : 1 - windowScroll / 570,
'background-position-y' : -windowScroll / 10
I think 'background-position-y' is only available in more recent versions of jQuery, and it may not work (I've just read..) in FireFox. I think there are plug-ins specifically for 'background-position-x/y'.
Added; Yes, put the whole of this code within the 'head' tag.