Sorry for the late reply here...
I can only offer advice with regards to OpenGL - but most of the ground lessons for 3D stuff apply equally everywhere.
First off: matrices. Learn how perspective and modelview matrices work, how the co-ordinate systems work. Trigonometry will definitely help, as you'll definitely be working with vectors.
Google is your friend - I suggest finding some OpenGL (or d3d if you want) tutorial sites. Two off the top of my head are:
http://nehe.gamedev.net
http://www.swiftless.com/opengltuts.html
(beware: they may concentrate more on OpenGL 2.x, but that may not be a bad place to start with anyway).
If I were to start again, I'd probably make a simple program (from the tutorials) up to applying textures and moving the camera around, and then make a transform (matrix) and vector class in (pick your language) to replicate OpenGL 2.x behaviour (great way to learn things is make them yourself). Start going into OpenGL 3.x from there (learn shaders) and by then you should be good to go on your own.