Swelling in the extremities (feet, hands, legs, for instance) is called edema. This is generally caused by fluid buildup around your body's tissues as a result of poor circulation or injury. While swelling can be an uncomfortable condition, there are some things that you can do at home, without medication, to relieve your discomfort.
How to Reduce Swelling
Some of the most common suggestions for reducing swelling can be remembered in the acronym R.I.C.E. This stands for rest, ice, compression and elevation, and you should do each of these things in that order.
According to The Doctor's Book of Home Remedies, you'll want to rest your hands first. This would be a good time to use an ice pack as well (ice). In a pinch, you can use a bag of frozen vegetables, preferably something small. (Peas are generally recommended because they are tiny and conform to the contours of your body easier than, say, a bag of frozen broccoli.) Use an Ace bandage, or even a good-sized hand towel, to compress the ice pack. Wrap your ice pack enough times to apply pressure (compress). Use a recliner, or simply prop your feet up on a couch or bed (elevate).
Also, because the swelling is in your hands, you'll want to avoid things that require gripping. As you probably need to use your hands and wrists fairly often, you may want to do some additional things to relieve the swelling. The Doctor's Book of Home Remedies again suggests staying active after exercise and swinging your arms back and forth. Both of these will keep your circulation moving, which will help prevent swelling. You can also try to shake it out. (Shake your hands and wrists frequently.) It's pretty common to have swelling of the hands and wrists in the morning, particularly if circulation is inhibited by the way you sleep. (For instance, if you tend to sleep with your hand tucked under your head, you may experience swelling or a sense of your hand "falling asleep" when you first awake.)
Considerations
Edema can also be a symptom of a more serious condition, such as heart, kidney or liver problems. Keep an eye on whether the swelling is regular or unrelieved with these suggestions. If none of these things help, or if you consistently experience swelling, you should see a physician.