I'm not sure if this is the right place to post your question. Some internet forums specialized in opengl might be a better place to get an answer.
but if it can help (I'm no expert)...
reflections ... it is what a graphics engine needs to simulate (be it based on opengl, directx, ...). Even raytracing graphics engine would be doing the needed operations to calculate the reflected eye-ray and the final correct color of the pixel at certain screen location.
I'm not aware of any 'magic' solution for this unless you are using a ready-made graphics engine.. but this I think is not what you want to do.
There are different ways of having the reflections (stencil, cubemaps, ...) and you need to see where and what for you want to use the reflections to be able to pick the right method.
Try googling a bit more and have fun building your own solutions to these kind of problems.