Public transport in Oman is limited to minibuses and long-distance coaches at present but there are ambitious plans in the pipeline for a rail system to link various places in the Sultanate, designed to carry both freight and passengers.
For travelling around Muscat, you can catch one of the white minibuses, which operate their route up and down the length of Sultan Qaboos Street and stop at designated bus stops. Fares are inexpensive and their regularity means you will never have long to wait if you have just missed one.
Coaches are used to travel to far away destinations such as Salalah and Dubai. The journey may be long as a result of all the bus stops along the route but the fare is not expensive and the departure and arrival times are fairly accurate. The journey starts at the depot in Ruwi so it might be a good idea to start yours from there too, if you want a better choice of seat.
The orange and white taxis could be considered as public transport as they appear to reach every area in Oman and they will conveniently take you to the door of your destination.
Female travellers should exercise the usual safety precautions when using public transport.