You can simply use a sphere-map.
The problem with spherical environment mapping is that they have ugly distortions on the back-side, but I guess this won't be a problem in your case as the view-point seems to be fixed.
All you need are proper vertex-normals and OpenGL will handle the rest:
glEnable(GL_TEXTURE_2D);
glBindTexture(GL_TEXTURE_2D, envmap);
glEnable(GL_TEXTURE_GEN_S);
glEnable(GL_TEXTURE_GEN_T);
glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_SPHERE_MAP);
glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_SPHERE_MAP);
// render
glDisable(GL_TEXTURE_GEN_S);
glDisable(GL_TEXTURE_GEN_T);
GL_SPHERE_MAP reflects the view-vector (camera to vertex) at the surface-normal and projects it into spherical coordinates, so the environment-map represents the reflective (specular) part of the light.
If you want diffuse lighting, you can use GL_NORMAL_MAP instead (and use a very blurry texture) - or even both.
Setting up a proper sphere-map works like this:

You can find many of those on
Paul's site.
If you want inter-object-reflection it's going to be a bit trickier, though.