From your description it sounds like you have a condition called focal hyperhidrosis - which means you are having focal sweating for at least 6 months (in this case your palms).
So there are several ways you can try treating this condition. The best advice would be to see your family doctor
regarding this issue, as he/she can best manage it can keep a close eye on it for you.
First, and probably the least invasive method, of treating this condition is to go to your local pharmacy or supermarket and buy some antiperspirant. Simply applying this to your hands can stop them from sweating as much, and some people find relief simply by doing this. If this doesn't work, there are prescription strength antiperspirants available as well - but you'd have to check with your family doctor before applying them. The one caveat is that you may get some skin irritation on your palms from applying this remedy.
There is no proven pill to help fix this issue. There is a pill that seems to help with hyperhidrosis, however, there hasn't been any conclusive data or evidence to suggest it works. Other treatments include botox injections, and even application of a current of electricity to your palms. Needless to say, this needs to be evaluated by your doctor who can help you better dictate your treatment.
Finally, in the worst case scenario, there are surgical procedures that can be performed to help with the condition.