Our 15 year old cat, who spends about 90% of the time outdoors in good weather has recently started to urinate on the carpet. We have taken her, shut her in a tile room with a litter box, food, and water and hope she gets the idea. Any advice on how to reteach her to use a litter box? She did for years, then became a predominantly outdoor cat, and relieves herself outdoors, but now she is staying in because of the cold and smelling up the house. Something needs to be done.
Before you do anything else, go see the vet. Sometimes carpet-peeing is a sign of a urinary tract infection in cats.
What antigen said. It can also be a sign of other things worse than a urinary infection. Especially in a previously well-behaved elderly animal. Poor kitty. She is probably in pain. 
Just to set the record straight, she has been to the vet and is fine. She just does the carpet stuff when she can’t go outside. We stuck her in a tile room and since then she has urinated in the litter box twice. Now we just have to figure out how long to keep her isolated. Anyone have any idea how long it will take for her to start using the litter box all the time, that is to seek it out, and not just go anywhere when she can’t get outside. We have a second litter box that our other cat uses, it is clear she doesn’t like to share.
Well, I’m glad your kitty is healthy. In one of my dear departed cats, the urination problem was the first sign of Something Much Worse.
Presumably you’ve been making sure that both litter boxes are as pristine as possible? Have you always used the same type and brand of cat litter? Some cats develop a preference or aversion to a particular litter. Also, be sure that wherever there was an “accident” that you take every conceivable step to eradicate the odor (difficult to do). If the scent remains, the cat interprets this as indication that this place is OK. Many pet stores carry cleaners designed to help with this.