Salt's old town is small enough to walk entirely. The streets are steep in places and the lanes narrow, but everything of interest is within about 15 minutes on foot from the main square. Wear shoes with grip — the limestone paving stones can be slippery when wet.
Beyond the old town, shared taxis run to surrounding villages including Fuheis and Ramtha. The town is not large enough to have a formal bus network. Taxis are cheap and drivers generally know the key landmarks. Some of the outlying shrines in the hills require a taxi or private car to reach.