My shower faucet handles are completely turned off but hot water continues to drip (alot) from the shower head. I took off the shower head and water runs directly from the spout. It seems I can't close the handle any tighter so what do I do?

Sounds like you need to replace washers and seats in faucet. Describe faucet, sounds like two handle.

Yes it's a 2 handle. I just too off the faucet knob and face plate that was against the tile wall. Now I see a white long plastic piece with threading which the wall plate came off. How do I remove what I need to replace (or clean out). Tahnks so much by the way

You should be able to unscrew the plastic, threaded thing by unscrewing with your hand. It may not be necessary to remove this however. Next you should see a bonnet nut or stem nut. That's the thing you tighten to prevent water from coming out around the stem. Next you should see the shoulders of the valve stem. That's what you want to unscrew. If these are back up in the wall you will need a set of tub wrenches. Tub wrenches look like a big cheap sockets, because that's what they are. They are sold in sets at home centers, hardware stores, and plumbing supply. Using a tub wrench unscrew the valve stem. You will also need a seat wrench to remove the seats. Remove stems and seats, take to hardware or plumbing supply for replacements. There is probably a 1001 different sizes, shapes and threads of seats.

You should be able to unscrew the plastic, threaded thing by unscrewing with your hand. It may not be necessary to remove this however. Next you should see a bonnet nut or stem nut. Thats the thing you tighten to prevent water from coming out around the stem. Next you should see the shoulders of the valve stem. Thats what you want to unscrew. If these are back up in the wall you will need a set of tub wrenches. Tub wrenches look like a big cheap sockets, because thats what they are. They are sold in sets at home centers, hardware stores, and plumbing supply. Using a tub wrench unscrew the valve stem. You will also need a seat wrench to remove the seats. Remove stems and seats, take to hardware or plumbing supply for replacements. There is probably a 1001 different sizes, shapes and threads of seats.
Follow the great advice Harold gave you. Here's a exploded view that might help.
Good luck, Tom