Orthonormal Basis question

Okay, say you have an orthogonal basis on a weighted inner product. If you're going to try and find the corresponding orthonormal basis, should you be going off the weighted inner product or the regular inner product? In other words, if I'm trying to find ||v||, should I be finding it using the weighted inner product, or just the regular inner product thing?

I'm trying to be general with my explanation so that I don't get the finger-pointing "DO YOUR OWN HOMEWORK", and so that I can still understand the concept. If I was unclear, I can actually post the problem that I have a question in.