If you have water leaking from your tub spout, you need to determine the root cause. Does the spout leak when the water is turned on or does it leak when the water is off? If your tub spout also has a diverter on it to shoot water to the shower head, it is common for some water to leak out of the tub during the shower, as the diverter usually doesn’t do a perfect job at stopping all of the water.
A valve behind the handle controls the flow of water to the tub spout. If water flows out of the spout when the handle is turned off, the problem is with the valve, and not the spout. You likely need the cartridge replaced (if a single handle valve) or the stem and seat replaced (for separate hot and cold handles). If water leaks from around the spout when the water is on, you need to check the tub spout and see if it is installed correctly. Tub spouts are either threaded on, or there is an o-ring that seals out leaks. These connections can get corroded and nasty, so maintenance is common. You will also get a leak if you try to rotate the tub spout once it has been installed, so once is it on, leave it alone unless you have a problem.
When you lift up on the tub spout diverter to direct water up to the shower head, does water still pour out of the tub spout? You probably need to replace either the gate in the tub spout, or just go ahead and replace the entire spout altogether.
You will find that the finding a replacement gate will be the hardest part of the job, which is why most people replace the entire tub spout. You can try contacting the manufacturer for the part, but for under $20 you can buy the entire spout.
If you are able to get the right part, you can replace the gate without too much difficulty. The knob that sticks out of the top of the spout will unscrew. You will probably need some needle nose pliers to reach up and pull the gate out. The new gate will fit back in its place. The gate will slide into some grooves that will help it stand up to the water pressure. The gate will only go in one way, so it helps to take note of how the old gate was oriented into the grooves.
Much of this is by feel. When the gate is in place, you can install the knob and then give it a test. When you let go of the knob, it should immediately drop down into position. This will allow water to flow into the tub when you turn the water on.
Replacing a bath tub spout is a two step process, removing the spout and replacing it. Removing the spout can often be the most challenging.
The challenging thing about removing a bath tub spout is that you don't know exactly how it removes.
The bath tub spout may simply unscrew from a threaded nipple sticking out from the wall, or it may be held in place with a set screw from underneath the spout.
You can certainly try to goose the spout free by gently turning it counter-clockwise. If it doesn't want to budge, don't force it...yet. If the bath tub spout doesn't have a set screw, then you can apply some muscle to it.
Look under the spout for a small hole. Inside the hole may be a setscrew that holds the spout to a bare copper pipe. You can use a flashlight and a mirror to see inside the small hole, or you can attempt to stand on your head.
If you can see a small hex head screw, use an allen wrench unscrew it. Sometimes it is a little tough to find the screw head with the allen wrench, but keep at it. Once the screw is loosened, you should be able to pull the bath tub spout free of the pipe.
If you need to replace a tub spout, you may find it a challenge to remove the old one. Tub spouts connect in a variety of different ways, and some are easy and some more challenging.
The old tub spout may simply unscrew from the nipple sticking out of the wall, or it may be attached to a bare pipe and held in place with a setscrew. It’s smart to get a small mirror (like a small cosmetic mirror) and hold it underneath the tub spout. This is where the set screw will be, if your tub spout is held on using one. Angle the mirror so that you can see the bottom of the spout and look for the screw. If you see the screw, use the appropriate sized allen wrench and remove it from the tub spout. This will allow you to pull the tub spout free from the bare copper pipe. It uses a rubber O-ring to keep the water from leaking, so you may have to put a little elbow grease into it.
If there is no set screw, the tub spout should be attached to a threaded fitting. Try gently unscrewing the tub spout from the threaded fitting coming from the wall. These fittings can be in either ½” or ¾” diameter, although ½” is far more common.