If you want to learn how to write graphical programs for a GPU, you'll use
HLSL (
via Direct3D),
GLSL (
via OpenGL), or
Cg (
via either).
However, you don't write full programs in these languages -- you only write small functions (
such as to colour in a pixel, or move a vertex) which are called by Direct3D or OpenGL, so you also have to learn how to write D3D/GL programs on the CPU as usual.
The small GPU programs/functions are called "shaders", and GLSL/HLSL are "shader languages".
Your GPU supports Direct3D 10.1 and OpenGL 3.3, which both in turn support fairly modern versions of the above shader languages.
If you want to learn how to use the GPU for non-graphical uses, then you're in the same boat, except the CPU-side APIs that you first need to learn are (
one of)
DirectCompute,
OpenCL or
CUDA.