Soap and water... Kids who perspire a lot is not necessarily abnormal. I would just keep them as clean as possible. There is a condition called hyperhydrosis but it usually involves the entire body. Consult your pediatrician for more information if the concern persists.
Drying measures. For the most part, moist palms and soles of feet can be dealt with by simply keeping the surfaces clean, wearing absorbant socks, and putting a tissue in pockets so they can dry their hands. If there is beginning to be skin breakdown, peeling, itching, cracking, then a clear deodorant can be lightly applied to palms and soles. For severe skin reactions to sweat, drysol works well.