The content of Quake III is completely separated from the engine which drives it. You can make your own maps, characters, sounds, bots, behaviors, textures, etc.
You'll need to download the map editor, Q3Radiant, in order to create maps for Quake III. This is the official editor used by id itself. To learn how to use the editor, try these:
Q3Mods.net - they have excellent tutorials on all of the basics and some more avanced concepts.
Rungy's Metropolis - this is a sub-site on Q3Mods and has a tutorial showing you how to make a city! The menus indicate that more will be added too.
Rust - There's a section called 'Tutorials' here. Obviously, Quake III is the most useful, but the Quake II and General Editing Tutorials deal with Quake II editing, which for basic editor usage is the same as Quake III. All of the effects are done with shaders now, though.
q-workshop3 - Newbie AND advanced tutorials
Ricebug - advanced curves and more...
QERadiant - promises tutorials, but none here yet.
Dragon Turd - Some good stuff with special effects and func_ entities.Gothic Tutorials - detailed tutorials of arches, etc.
Claudec's Lair of Shaders - Some textures, lots of specific tutorials on curves, etc.
Astrocreep - some prefabs, hints.
Custom textures and shaders
There are many things you can do with a texture to get different effects. Behaviors for a texture are attached via scripts called shaders.
An older site, Maj's shader tutorial, which is no longer supported may also have information you're looking for.
F Vs. F has some tutorials on coding
Q3Seek has a bunch of tutorials and is in PHP!
Primordial soup - textures and other resources