Test the faucet by turning the water back on at the shutoff valves and make sure that you can turn the stems with the handles and to see if this did anything about the leak. If it did, great!! Put everything back as it was. If it did not, TURN THE WATER OFF AT THE SHUTOFF VALVES AGAIN. Then open the faucet a little to release the pressure of the water in the faucet.
One thing that you could already have or will run into, depending on the design of the faucet is trim pieces. These generally unscrew on pipe threads, one way or another. They could also just snap into place. You want to look all around the faucet and trim parts to see if you can get an idea of how they are put together and how they come apart. Again, there are so many designs and manufacturers that "one size fits all" statement are impossible. You probably can remove most of the trim parts by holding them in your hands and turning counter-clockwise.
One of the main jobs of the trim rings is to cover the edges of the hole through the tile and backer board in the wall. If this is soaked with water, you may have to replace tile or you may not. Unless the tile is already falling off, you may not know for sure unless everything has had a chance to dry out. There is a lot of info on replacing tile in this situation on this forum and others. I'll let others cover this because we still don't know if you have to. In any case, keep all the tile that comes off and try to label it for location. A "map" of where which piece of tile came from can be a big help later.
On to more on the leak--. With the trim pieces off, you should be able to see the top of the bonnet, the piece that the stem sticks through and that holds the insides of the faucet in place. Using the right sized one of the big sockets I mentioned above, unscrew the bonnet. If this is a Delta faucet or similar, it will have a plastic and metal assembly called a cartridge that will come out with the stem on it. It will have a plastic bump on the side that fits into a slot in the faucet body. Remember where the bump was positioned and this will be different on each side. Now take the whole mess to the home center and tell them that you need a replacement cartridge for each side that leaks. It will have several parts in it and great instructions for replacement.
Other faucets have stems that have a rubber washer held to the bottom of the stem assembly with one screw. The rubber washers can be either flat or conical. When you get these stems out, take them to the home center and tell them that you need a match. These will not come with any instructions, so tell the clerk to tell you as much as he can about the brand it is, size washer, condition of the other parts in the assembly and anything else that he thinks is important. When you get home, replace the washer and the screw with new ones on each faucet assembly. Put the faucet back together in the reverse order that you took it apart and by turning all the threaded connections in the opposite direction from how they came apart. This should fix a drippy faucet. Turn the water on at the shutoff valves and be prepared to shut if off quickly if you still have a leak or there is water gushing. Gushing is probably easier to fix because that means that you didn't put something together right or a part is broken. (Don't call me or cuss me, it is a lot easier to fix many things than to tell someone else how to do it.)
If the leak is coming from anywhere but from around the stem or it's just a dripping faucet, you probably can't fix it. This will require calling a plumber. Be there when he comes and watch what he does, particularly if he takes the faucet apart, so you can see how it's done for the next time.
Angie, you did not really give me much to go on since a leaky faucet can be caused by so many things and there are so many different brands and styles. Being more specific helps both of us. A big part of do-it-yourself projects is knowing what not to do yourself also.