First thing to know: if the shower drips for a minute or two after you shut it off and then stops, that is just water draining from the arm and head by gravity. Not a leak. But if it keeps going -- even slowly, one drip every few seconds -- the shower valve is not closing all the way. The cartridge or washer inside the wall is worn and letting water seep through. Single-handle valves (Moen, Delta, Kohler) need a new cartridge. Two-handle valves need new washers and possibly new seats. There is also the much simpler scenario where the drip is just at the threaded connection between the shower head and the arm -- that is a 5-minute Teflon tape fix.