You can get to salalah via Dubai Via Muscat by Bus Transport. From Dubai you can catch a bus to Muscat for as low as US$13 from Deira Dubai ( Behind Dnata - Emirates Building Near Clock Tower Roundabout ). Upon reaching Muscat you can change the bus going towards Salalah. It takes 5 hours from dubai to muscat and then further 10 to 14 hours to salalah.
Bus transport around salalah is no available and you have to rely on local taxis which are cheap.
We hired a car from Thrifty for OM 12 per day (OM 2 was for insurance). You get 200km free, after that its 500 baiza per km. All the other companies in town only give 150km free, and some charge up to OM 15 per day for a car.
Best, and quickest option is to fly.
Alternatively drive (8 - 9 hours) - only interesting for the first 2 hours and the last 1 hour - through the mountainous sections. The rest is billard table flat!
Better still make a trip of it and take a 3 or 4 day 4WD trip from Muscat along the coast. Plenty of food and fuel required.