Look for a general "fitted pad" if you have a standard-sized mattress. It's made like a bottom sheet in that it has elastic corners to hold it in place. Choose a "guaranteed-to-fit" mattress pad if your mattress is a deep-pocket type. This pad has elastic around the sides to help hold it securely in place.
Decide what type of fabric your mattress pad needs to be made of. Cotton pads, for example, provide breathable comfort. You can choose hypo-allergenic pads, as well as waterproof ones. You can choose a plain cotton pad that won't add height to your bed. Or, you may want a filled pad to add comfort.
There are also visco elastic mattress pads, fiberbeds, featherbeds and convoluted pads. The visco type is a foam that conforms to your body. Fiberbed and featherbed mattress pads add soft cushion. And, the convoluted mattress pad resembles an egg crate with its series of indentations. The indentations are designed to distribute your body weight more evenly so you experience a restful night of sleep.
Check and compare the cleaning instructions on each type of mattress pad you are considering. Cotton and other types of fabric pads can typically be washed in a machine. To clean a foam or convoluted pad, you'll need to perform the task by hand.