Keeping your elbow at a good angle will help (somewhere where your shoulders are relaxed, but not too low or you'll start getting shoulder pain) with one of those gel wrist support mouse-pads will help. Don't know if you have one, but gamer mouses (mice? Why can't it be mice for pc ones too?) are a godsend. If you've got your average 2/3 button mouse that comes stock standard, chuck it. It's not big enough for your hand. Find one that feels comfortable and that you can change the weights. My one has buttons on the side so my index finger can take a break.
Once you actually get the pains in your hand, take a few minutes to clench then unclench your fists, shake your hands then stretch your fingers back one hand at a time (this will also stretch the muscles in your arm and increase blood flow).