Get jQuery up and running in a minute or less:
Insert this into your HTML (most commonly in the head, but you can throw it before the end body tag too):
<script type="text/javascript" src="http://code.jquery.com/jquery-latest.min.js"></script>
Then place a script element after your jQuery one. This would alert 'hello' after the DOM is ready.
<script>$(function() { alert('hello') });</script>
Read the documentation.
Using jQuery locally:
After you get a feel, try downloading jQuery locally to your computer, and link it from your script file. The structure is like so:
C:/web/index.html
C:/web/js/jquery.js
index.html:
<head>
<script src="js/jquery.js"></script>
<script>$(function() { alert('hi') })</script>
</head>
You have the advantage of relying on your saved version offline if you don't have the Internet/Wi-Fi. You can also make custom edits to the jQuery source and modify it at will.
Study the jQuery source [advanced]
Download the uncompressed version from:
http://code.jquery.com/jquery-latest.js
After you've gained a bit of JavaScript/DOM knowledge try to take it apart step by step.