Many people have questions about how to litter box train there cat. The great news is cats usually come litter box trained along as you don't already have a trouble maker.
However, if you are just bringing a new cat into your home it is always best to hope for the best and assume the worst. In this case whenever you are not watching the cat confine him or her in a nice room that is, it's okay if they soil, like a bathroom is a common place. It is easy to use a small place because you can easily cat proof it until you know what that cats personality is. Now when you put that litter box out make sure you have enough litter in that pan, at least two or three inches deep is a good way to go, Keep in mind research shows us that most cats prefer unscented lump and clay litter and other cats may have different preferences. If you find your cat isn't using the box try alternating the box with the litter itself and see if that will help your cat be interested.
If you run into troubles it is always a good idea to give your cat a treat just as he or she is coming out of the box so that way you can associate going to the bathroom in the box with something special. Remember sometimes use the box as a place to catch the cat for all sorts of things that the cats don't like. Taking pills etc, if you are bringing a new cat home you might have to undo all that work that was done before they came to you. And that's how you work on litter box training your cat.