A leaky shower wastes water and, when water escapes the enclosure, can rot the structure behind the tile. The fix depends on where the water is coming from.
Dripping showerhead
A showerhead that keeps dripping after you shut it off usually means a worn valve cartridge or washer inside the faucet, not the head itself. Replacing the cartridge (shut off the water first) stops the drip. A head leaking at the connection just needs fresh thread tape.
Water escaping the enclosure
If water ends up on the floor outside, the culprit is often failed grout or caulk, a gap at the door or curtain, or a worn door sweep. Re-grout and re-caulk cracked joints, and make sure the door seals and the curtain tucks inside. Water behind tile from failed waterproofing is more serious.
Leaks behind the wall
Stains on the ceiling or wall below a shower point to a leak behind the tile — at the valve, drain, or failed pan. These need opening up to diagnose and are often a plumber's job, since the longer they run the more hidden damage they cause.