First, soak up as all of the urine. Use paper towels, a weight (an old heavy book works well), and apply pressure to force the stain at the base of the carpet into the towel. Douse the area with cool water and soak it up with paper towels again. Repeat until the area is clean.
Pet trainers recommend placing the urine soaked paper towels in the area you want your pet to claim as their bathroom, ie: the litterbox, nespaper, or outdoors. Your pet uses its sense of small to determine where to relieve himeself or herself and moving it where you want them to go reinforces the training. Always use positive renforcement and praise for your pet when training.