Excess sweating on the palms, soles of your feet or even face is known as hyperhidrosis. While sweating on the face, chest and back is generally due to heat, sweating on the palms and soles of your feet is usually due to emotional stress.
Some medicatiosn can exacerbate hyperhidrosis, so if you're taking anything - have a chat with your pharmacist or doctor about the potential of it causing the problem.
Some people find that using a high strength aluminium antiperspirant (e.g. 20% aluminum chloride in ethanol) product can provide relief for up to 24 hours; and they can be used on your palms/hands/feet i.e. not just your arm pits. One such product is Drysol which I've personally used before and found great for reducing sweating. Usually you put it on nightly for a week or so (and washed off in the morning), and then you can use it less often afterwards.
Alternatively, there's other treatments that use low electrical currents or local injections of botox. Sorry I don't know a lot about them or how effective they are. If you find that stress is what's causing your sweating, sometimes taking medications to reduce your anxiety can also help. I'd suggest you have a chat to your doctor about it.