Cars can be hired at the airport as well as in the main population and tourist centres and on Gozo. Most hire companies will also drop off and pick a car up, sometimes without additional charge. If you are at the younger or older end of the adult age range, be warned: many hire companies in Malta require you to be 25 in order to hire a car - although some will hire to you from 21 - and if you are 70+ you may be asked for a medical certificate stating your fitness to drive.
It is worth shopping around; prices can vary considerably from company to company. Some charge extra for a second driver and insurance costs vary too. Think carefully about insurance. The Maltese are not the most careful drivers in the world. In fact the only truly predictable thing about driving in Malta is its unpredictability, so be on your guard.