What can I do about swollen hands?

Hydrate. Unfortunately, there is not much that can be done for benign swelling related to pregnancy. Staying hydrated and decreasing salt intake will help. Be warned that swelling usually gets worse right after the baby is born, then improves over a few weeks postpartum.
First determincause. Although it is likely to be benign, the cause may be reflective of some more serious underlying condition such as vascular compromise, lymphatic obstruction, auto-immune disease, allergy, nutritional deficits, etc. This should be evaluated by your primary care physician first. Otherwise compressions and elevation are the mainstays of therapy.