One of the most frustrating things in life, at least in my opinion, is when kitty refuses the litterbox and wizzes on the carpet instead. As a cat owner with experience in dealing with felines that show litter aversion, I found several techniques in dealing with this problem.
1) First, make sure kitty doesn't have a urinary tract infection or kidney stones. How can you tell? You'll find kitty squatting in odd areas on the floor, straining to urinate. You'll also find tiny spots of urine around the house where kitty tried to go, but couldn't. With a urinary tract infection, you'll also see reddish blood spots in the urine. If you suspect any of the above, take kitty to the veterinarian.
2) Take note when kitty begins to sniff in corners or along a wall. These are the preferred places for kitty to urinate. If the cat sniffs excessively and maybe meows a little, and especially if kitty starts digging into the carpet with his/her front paws, immediately pick him/her up and plop kitty in the litterbox.
3) Line walls with pillows, chairs, or a plastic runner to block off that area of the floor. This will force kitty to use just the litterbox.
4) Keep litterbox clean. This is critical! Cats are very picky creatures, and like to be clean. Many people don't bother to scoop daily, but the truth is litterboxes should be scooped twice per day.
5) Use clumping litter. Traditional clay litter theoretically needs to be dumped once per month with the poop scooped daily. However, I've found that after only a few days kitty is turned off by foul odors. Clumping litter means the urine forms clumps which are scooped out daily, thus no odors.
6) Use a litter type the cat likes. Cats generally like sandy litter that they can dig in and paw. Clumping litter is great in this respect. You can try crystals, recycled newspaper litter, pine, and those corn-based litters, but your cat may not agree. (My cat once began to eat the corn-based litter!)
7) Use two litterboxes per cat. In multiple cat households, this may not be practical. But I have found that kitty is much more amenable to using the box when she has a choice between two boxes; one in the kitchen, and another in the bathroom.
8) Cats generally return to the area they wizzed in. When kitty goofs up and wizzes on the carpet, immediately soak up the urine with a paper towel. Lift up the carpet and wipe the backing, then soak up any urine that soaked into the carpet padding. Now spray a stain remover on the carpeting and scrub; do the same for the backing and the padding. I use Spot Shot, and it seems to work pretty well. Failure to attend to urine spots immediately results in the familiar "cat smell" so familiar in cat owners' homes.
9) Plop kitty in the litterbox at any time. Maybe she'll go, maybe she won't; but at least she'll understand where the box is and what it's for.