combining textures and colors

I know how to do simple texturing in OpenGL. But let’s say I want to draw a polygon, made up of 4 vertices, and textured with some nice image, but for each vertex, I want the texture to be darkened by some amount. Maybe the 1st vertex I want full brightness, 2nd vertex I want 0.7 brightness, and the other two vertices I want 0.3 brightness. And then the stuff in between the vertices is interpolated. How would I do this?

Try using glTexEnv with GL_BLEND. You may need to tesselate your quad to get the effect you want.