The most common cause of a leak from the handle is a loose stem packing nut.
If you examine the handle you may see a snap in plastic cap in the center of the handle. If so, you should be able to carefully pry the cap out and there should be a screw under the cap that holds the handle in place. First remove the screw, the slide the handle off the valve stem shaft. You may be able to access the stem packing nut without removing the trim escutcheon. If not, most of the escutcheons slip off, although some are threaded in place. Either way it should be easy to determine which type of mount and it should come off easy.
If you do not have a center cap look on the underside of the handle and you should find a set screw. If it is a set screw it may be a recessed hex type screw and will require an allen wrench to loosen the screw. If you have a set screw type you should be able to just unscrew the set screw enough to loosen the handle without actually removing the set screw.
Once you have the handle off, and if necessary the trim escutcheon, you will see a nut on the end of the valve body surrounding the shaft to the handle.
You should be able to use an adjustable wrench to tighten that nut slightly by turning it clockwise while facing the valve. Tightening the nut will compress a packing under the nut tighening the packing against the shaft. Tightening the nut is really a bit of a judgement call because it must be tight enough to form a proper seal around the shaft but tightening it too tight will make it difficult to turn the handle. You can slip the handle into place and test it while tightening. Once you have it tight enough to stop the leak, replace the trim escutcheon and handle in the reverse of the manner you took it off.
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