At the time of writing a new bus system was being introduced in Muscat and between cities – a welcome move in a country that has very little reliable public transport.
Long-distance shared taxis, painted orange and white, and microbuses (hard to use without some rudimentary Arabic) travel between most major towns. They do not wait until full to leave – drivers pick up and drop off passengers along the way.
For most places of interest, it's only possible to take an ‘engaged’ taxi (ie private, not shared) – four times the price of a shared taxi to cover the cost of the empty seats. Settle the price before you get in and expect costs to vary.
Beware that public transport isn’t networked yet – a bus or taxi may go from A to B and B to C but not from C to A. This means it’s easy to get stranded in a town with no onward connections.