The frequency required for completely changing the litterbox varies, depending on the size of the litterbox, the type of litter being used, and the number of animals sharing the litterbox. Most litterboxes need to be changed around twice a week, but your mileage may vary. Between changings, it is important to keep an eye on the litterbox and to scoop out feces on a daily basis to ensure that it is pleasant to use; if you don't maintain the litterbox, the user may choose to eliminate urine and feces elsewhere.
Basically, you need to change the litterbox when it is no longer usable. Many litters clearly indicate this by clumping or smelling especially strong when they are totally saturated with urine. While it's a good idea to set regular days to change the litterbox, it's also advisable to be flexible, as the litterbox may be dirtier at some times than others. Also, if you notice that your pet is reluctant to use the litterbox, you may want to change it, whether or not it smells or looks clumpy.
Many veterinarians recommend the use of a single litterbox per pet, as a general rule of thumb. This means that if you have three cats, you should have three litterboxes; having designated litterboxes can help to prevent territorial squabbles, and to reduce the number of times a week you need to change the litterbox. Be aware that some pets do not like to use a litterbox which has been used by another pet, and that placement can be important; you may need to move household litterboxes around a few times before everyone is happy.
When you change the litterbox, it is important to clean the litterbox in addition to dumping out all of the litter. Mild antibacterial soaps are ideal, as they will help cut down on odor and discourage any bacteria colonies from forming, keeping the litterbox healthier for the animal to use. Be aware that some soaps and cleaning chemicals are dangerous for cats, rabbits, and other litterbox users; you may want to read up on a list of potentially dangerous chemicals for your pet so that you can avoid using them.
After you clean the litterbox, allow it to dry completely before pouring in more litter. The use of a litterbox liner is not absolutely necessary, but it can make cleanup easier, and whether you use a liner or not, you may find that sprinkling some baking soda into the box helps to cut down on odor. If you use a covered litterbox, you may want to note the date when you change the litterbox on the calendar, as it's easy to forget about the litterbox when it is covered to reduce odor.