Is Google Chart API free to use? If so, where can I find its documentation?
Yes, it is free. It is written in the official page:
Completely free for all uses: commercial, governmental, personal or educational.
For documentation follow this link.
Edit: You don't really download it. You include the following in your code:
<script type="text/javascript" src="http://www.google.com/jsapi"></script>
Then you start using it as shown here.
If you really want to see how it looks like inside, you can paste this to your browser address bar: http://www.google.com/jsapi