[davidhollander]

Start by deciding whether you want to target a single platform or a list of multiple platforms, and then choose whether you want to work with 2D, fixed pipeline 3D, or programmable pipeline 3D.

For single platform 2D, research the platforms standard development kit. For cross-platform 2D, find a library exposing an API supporting all available platforms[1]. For cross platform 3D, create a list of hardware you wish to support and find the maximum common OpenGL\GLES version and GLSL shader version.

This should give you an idea of the graphics API you will be working with and need to learn.

[1] http://www.libsdl.org/ is one such library if you go this route, I believe it's used in Angry Birds and Valve's Linux port of Steam.