Although not totally natural, most cats seem to be born with good litterbox instincts. Even so, there are a few specific things you can do to improve your chances of never finding urine or feces in the middle of your Persian Rug.
Regardless of the size of your cat, get (or make) the biggest litterbox you can fit into your home. Cats love to have room to walk around, roll over, stretch, and scratch before they get down to serious business. A big box with lots of headroom is nearly always more inviting than a short, cramped container. Think Executive Washroom versus Honey Bucket.
Don’t be afraid to try different litter types. The most popular forms are the fine-grained clumping litters, the natural source litters (wheat or corn cob), and those produced from recycled papers. The least tolerated are any litter type with perfumes, scents, or other chemical additives, so try to avoid those if you can.
Just as in Real Estate, location is paramount. High traffic areas of the home are seldom a good choice, nor are rooms with loud noises like laundries and kitchens. Cold, cement floors leading to a litterbox are also a major turn-off for cats. Quiet, yet easily accessible are the goals to keep in mind at first. Feel free to experiment with more than one litterbox (in different parts of the home) for a period of time, to see if your cat displays a definite location preference.
In general, anything you can do to make the litterbox more attractive to the cat will go a long way in helping your pet to establish good habits, and keep your home clean.