The wordpress codex is its main documentation for use and customization. There’s a getting started section, sections on themes and plugins, and also on how to contribute and give back.
Contributing to the Codex – It’s written in a wiki fashion that’s easy to add to, edit, and track changes.
The Codex For Beginners – Under Learn How to Use WordPress, a great spot to learn. WordPress Lessons are in this section and are in depth articles with info on things like comments, floating images, etc. WordPress.tv hosts videos from wordcamps. WordPress semantics lists out common WP terms and what they mean.
The Codex for Theme Developers – Talks about theme development, which has info on everything you need to know to do that. Use the table of contents, which is auto created based on the page headers. There, the Stepping into Templates page talks about how pages are constructed. From here, the Template Hierarchy covers the major template files for home pages, post pages, etc and how they should be named/constructed. There’s a good diagram here that explains this.
Template Tags are the functions that are used in those files, and this page outlines them. Click on one to learn the details of how to use it (which actually takes you into the function reference, noted below). Note that these aren’t all the functions, they’re just the ones specific to working with templates. To see all of them, go to the Function Reference. Note that you can quickly modify the url to get to whatever function you want by putting it in at the end.
The Loop in Action Page goes over how the WP loop, the logic for displaying content in WP, is used, and how to customize it.
The Codex for Plugin Developers – Writing a Plugin covers basically everything you’ll need to know to write one.
The Plugin API Section is the homepage of where you’ll look up the actions and filters you can use in WP. The Action Reference and Filter Reference have a list of all the actions and filters available. Ones in red have no info yet, and could use some contribution. Adam Brown’s WP Webhooks Database is a popular site with a list of all the hooks used in WP.
Back on the home page, Plugin Resources gives general info on working with plugins, and links to articles written for plugin devs. It has a link to the Option Reference, and Database Description page, which has a graphic of all the major tables, rows and sections of the database, and how to Query it. There’s also the C Coding Standards, of which the PHP ones are helpful for plugin development.