What is the best way to get rid of swelling of the hands?

Ice and Elevation: In general, ice and elevation can be helpful to address any acute swelling. Over the counter anti-inflammatories such as alleve and Motrin can be helpful. However, if the swelling is chronic, then you should be seen by your physician.

Elevation, motion: Elevation of your hand above heart level is key, along with range of motion which acts like a pump to remove swelling. An edema glove from a pharmacy or therapist will help.