By ship
There is at least one operator in Muscat that will charter you to Salalah.
By bus
There are daily buses between all Omani cities, very cheap compared to the cost of taxis, airfare, etc. In August 2011 Muscat-Salalah was 6 R.O. and 11 R.O. for two way ticket--it's a 12 hour trip.
By car
It is possible to drive from Muscat to Salalah. The trip takes roughly 12 hours although there are numerous places worth a detour en route. From the starting point sure its a cheerful trip where you can enjoy the wild beauty. Rusayl, Nizwa, Haima, Thumrait and next is the most beautiful Salalah.
Watch out for renegade dunes on the way! When you get hungry, thirsty or tired, you should take the next opportunity to stop - there might not be another one for dozens of miles.
Driving to Salalah from Muscat can either be an amazing and memorable experience, or a very uncomfortable one depending on what kind of traveler you are. The first 5 hours will be very scenic, as you pass Nizwa and other towns. However, it's barren desert and oil fields for most of the remainder of the trip. Travelling at night is usually better than driving in the heat of day arriving in Salalah at night is a must - the city lights from the high-altitude entry point is gorgeous. There are several stops along the way for food, drinks, a cigarette break, or nature calls.