YOu state that the leak is constant even when the shower is not in use, therefore the leak must be on the supply side of the shower control valves. Unfortunately shower & tub mixers are the only fixtures that are not required to have indidual shutoff valves therefore in order to service a shower or tub mixer you must turn the water off at zone valves to the bathroom or at the house main shutoff valve. (many homes do not have zone valves).
There are two likely causes of you leak.
1.The stems have vibrated loose and water is leaking out though the stem mount threads.
2. The mixer is mounted in an outside wall in a cold climate and either the mixer body or the supply lines have frozen and ruptured.
Begin by turning the water off at a zone valve or the House main, then open the valves to relieve the residual pressure.
Begin by removing the screw that holds the handle on the stem (handle center). Then carefully remove the handle. If the handles have not been removed in a long time they may be difficult to remove. The preferred method is to use a "faucett handle puller" (available at all hardware stores for about $10).
Next remove the TRIM ESCUTCHEONS. Most of then are mounted on the stem body by means of a fine thread inside the brass tubing in the inner end while some are just slipped on by friction fit. In either case, carefully unscrew it in a counterclockwise direction and it should slip right off. If you must use a pair of pliers to turn it, wrap the escutcheon with a rag to protect the finish. (If you happen to have a vinyl strap wrench that would be best to protect the finish).
On the outer end of the stem there is a stem packing nut, that tightens the packing that seals the stem shaft. DO NOT TURN THE PACKING NUT).
Look in the hole and examine the stem where it is attached to the mixer body. If you see evidence of a leak around the base of the stem you may be able to correct the problem by removing the stems and replacing the nylon flat washer seals on the base of the stem. (Once you have the stem out take it to a local hardware store and they should be able to supply you new flat washers.)
Most stems have a set of flats like a bolt head molded into the body of the stem near the base where it is attached to the mixer body. You may need a set of plumbers sockets to remove the stem. (A full set of plumbers sockets is available at all local hardware stores for about $10).
The handle pullers, plumbers sockets and vinyl strap wrenches inexpensive common tools and would be handy in any homeowers DIY tool kit. Combining those with a set of screwdrivers and a pair of channel lock pliers will handle most common DIY plumbing projects.
If replacing the step mount flat washers does not resolve your problem you will have to open the wall to examine the mixer body and supply piping. NOTE: If you have tile, a fiberglass or vinyl enclosure it would be best to try to access from the backside through an adjacent sheetrock wall if possible as it is a lot easier to repair the sheetrock as the tile or vinyl enclosure.
