I have been doing the exercises every other day for several weeks. My problem is that my wrists are REALLY sore. Do wrists need to get stronger? Or am I doing something wrong like gripping too tight or bending my wrists? If this is a common symptom of doing something wrong, can you tell me? I really want to resolve it and stick with the strength training.

The problem could be your form; or it could be that your wrists are weak. If so, these suggestions should help:

First, make sure that your wrists stay straight and in line with your forearms when you're doing the upper body exercises, particularly the biceps curl and overhead press. It might also help to wear wrist braces for a little additional support. If you're interested in strengthening your wrists, try doing wrist curls (description below). I hope this helps. But if the pain worsens or continues, please see your doctor promptly, since there could be a physical problem that needs to be addressed.

WRIST CURLS