Go to the store if you have not already and pick out a litter box that would be right for both you and your cat. There are several different types of litter box's, there are big ones and small ones there is also an automatic cleaning box that has a scoop that will rake the dirty litter into a storage bag. Some people even use the disposable litter box's which come with the litter already inside so you don't have to touch anything.
Finding the right cat litter is a fairly straight forward task. There are a lot of different types of cat litter; you can choose between scented litter and non scented litter. There is also litter which will clump up after your cat does his/her deed making it much easier for you to scoop up. You should change your cats litter box at least every other day this will keep your house smelling fresh and clean.
It is not a good idea to place the litter box near your cats food. Cats do not like to eat in the same place or anywhere near where they have urinated. Also never clean the litter box if you are pregnant because it contains toxoplasmosis in the fecal witch has been known to cause harm to your baby. Cats have been known to urinate on clean places such as your couch or carpet when they have a dirty litter box. Ensuring that the litter box is clean is very important in training your cat.
Male cats should ALWAYS be neutered as they like to spray to mark their territory, this also helps with unexpected kittens. A mixture of vinegar and water will help to make the smell go away. You can use half water and half vinegar to clean this up. This will keep your cat from returning to that same spot to use it again.