Gozo has an extensive bus network radiating from the bus station in the centre of the capital Victoria, but the buses are not as frequent or as reliable as they are on Malta. In fact, in winter they can be pretty few and far between on some routes.
There are several taxi firms, some of which also hire self-drive cars. These include Frank’s Garage (+356 21 556 814, franksgarageltd.com) and Mayjo (+356 21 556 678, www.mayjo.com.mt). Driving in Gozo is less alarming than on the main island because the traffic moves more slowly and people are in less of a hurry.
Finally, Gozo is not very big (only a few miles across at its widest) so in good spring or autumn weather it is very pleasant to walk around, and a lot easier to do so than on much of Malta. There are some particularly good walks around the coast and neighbouring villages are often closer together than you might think.
For general advice on getting around Malta, see my How to get around Malta page.