The best way to reach Wadi Shab is to fly to Muscat and then drive to Sur.
It's best to fly into Muscat International Airport. From there, you can take a bus, rent a car, or hire a cab to take you to Wadi Shab in Sur.
It is best to rent a car and drive to Sur. The trip will take around 2 hours. You can rent cars from Speedy Oman, ArabiaCars or Sixt Rent a Car. Prices vary depending on what car you choose. All these companies require for you to show them your international driving permit as it is illegal to drive in Oman without one. Alternatively, you could hire a cab, but taxi drivers are a bit reluctant to drive that far.
From nearby cities. Talk about connectivity, compare different services (if any)
From Muscat, you can take a bus from Ruwi. Buses go at 7:30 as well as 14:30. The trip from Ruwi to Sur takes around 4.5-5 hours. It costs OMR 4.
From nearby cities.
There is no public transport that can take you from Sur to Wadi Shab. One will have to drive down in a private vehicle or hire a taxi.