Patater has created an incredible beginner's manual for Nintendo DS homebrew. In its first version it already covers the basics of the homebrew movement, hardware and software setup, backgrounds, sprites (setup, rotation, translating, loading, displaying), hardware I/O, game mechanics (acceleration, angles, geometry), and more. It's all supported by code or visual aids as well!
Off to a great start. Now I can finally get around to learning something besides framebuffer mode with a reference that isn't outdated.