jQuery
New Wave Javascript

jQuery has a comprehensive set of documentation - everything from specific methods with code samples to a step-by-step Tutorial.

API

Most of the methods that you might be interested in would be in the jQuery Base - but feel free to look at the other modules for the applicable information.

• jQuery Base - The core functionality of jQuery - all the essentials are here, including documentation for how exactly $() works.
• Basic Effects - A break-down of how the effects work, and how to use them on your site.
• Advanced Events - A number of handy helper functions are included for working with events, above and beyond what bind and unbind are capable of.

General

If you're looking for a good place to start, I'd recommend taking a look at the Tutorial, it gives you a number of popular scenarious, and walks you through the process of using jQuery.

If you're planning on using jQuery with Prototype, make sure you read this before beginning.

If you're wondering why jQuery looks so different, you might be interested in what we call Chainable Methods.

Also, if you'd like to extend jQuery to add your own methods, you'd be interested in developing a Plugin.