The whole idea behind a litter box is based on a cat's natural instincts. Kitty does its business, then covers it up. If your cat is choosing somewhere other than the litter box, there could be a number of reasons. First, rule out health problems. Have your cat checked for possible bladder or kidney conditions. Next, consider the box itself. Keeping it clean is a definite priority. Cats are naturally clean creatures and want an equally clean place to use the bathroom. If you have more than one cat, you should provide each with its own box. Consider the location, as well. Cats like privacy in such matters. Don't put the litter box next to a dishwasher or other appliance that can make loud, scary noises. Different cats will prefer different types of litter. Experiment with several types until you find one the cat likes. If you have a new kitten, introduce it to the box immediately. Lead your kitty to the box, rather than setting it down there. You want the cat to learn the route. Once it gets its paws in the soft litter, nature should take its course.
