The old city is best explored on foot. Many of the interesting lanes are too narrow for cars, and the distances between major sights are manageable if you're comfortable walking on uneven surfaces. Allow plenty of time to get lost — that's half the point.
For sites outside the old city such as the Towers of Silence and Dolat Abad Garden, taxis are the easiest option. Agree on a price before you get in; many drivers will offer a half-day tour of the outer sites for a fixed fee, which is often good value. Bicycle rental is available through some guesthouses — the city centre is flat and manageable, but the summer heat makes cycling an early-morning-only activity.
Motorcycle taxis (motortaxi) operate throughout the city for short hops. Regular city taxis can be flagged on major roads. Yazd does not have a metro. The city's main sights are concentrated enough that most visitors need a car only for the desert sites on the outskirts.