How long does it take testosterone replacement therapy for hypogonadism?

Depends. Testosterone replacement is done in many different forms for men and at different starting points. How quickly a man will feel a difference depends on the type of replacement used and his baseline. In general most men feel a difference within 4-8 weeks. If you do not, you need your levels checked anyways at 3months but do it sooner to adjust your medication.
It depends. I assume you're asking how long once you start t replacement before you start feeling better. If that is indeed your question, then it depends, mainly upon how poorly you felt and how much you're getting in replacement. The greater the difference, the shorter the amount of time for you to feel better. Think in terms of how much gas you put in your car. It depends upon how empty is your tank.