If your shower water is coming out both the tub spout and the showerhead, the problem is not with your tub faucet; it's the diverter. On each spout is a valve called a diverter, which prevents water from coming out the spout and redirects it up through the showerhead. When this part breaks or fails, the entire spout needs replacing because the stop is part of the assembly. You can replace the spout quickly with no special tools.
Turn off the water in your shower by shutting the water valve on the main incoming water pipe, which is likely near your water heater. Twist the valve clockwise completely.
Look for a small screw at the base of the spout near the shower wall end. If you find one, loosen it with an Allen wrench and slide the spout off the pipe. If there is no small screw, your spout is a screw-on variety. Simply twist the spout counterclockwise to remove it. If the spout will not unscrew by hand, insert a screwdriver in the spout mouth and turn it for leverage.
Unwind the plumber's tape around the threaded end of the shower pipe. Wrap new plumber's tape around it about three times. Slide the new spout over the pipe.
Screw in the new screw to secure the spout in place, or turn the spout clockwise to thread it onto the pipe threads. For added protection, seal the edge of the spout by running a bead of silicone around the seam of the spout and shower wall.