By bus
There are two roads to Mae Salong: one from Pasang, a hamlet on the Chiang Rai-Mae Sai highway, and one from Tha Ton, on the northern border road from Chiang Mai. Both are scenic and very twisty — pop a pill beforehand if you're prone to motion sickness.
From Chiang Rai, take a bus to Mae Sai platform 5 and ask to be dropped off at Pasang/Mae Salong. The trip costs 25B and takes approximately an hour. Beware: there's another Pasang to the east of Chiang Rai, signposted at platform 9, but this will take you in entirely the wrong direction! At the Pasang T-junction, there are blue songthaews that leave when they get 8 passengers at 50 baht each, or when somebody ponies up the 400 baht to charter. Try to get here as early as you can, since otherwise, especially in the off season, you'll be looking at a long wait.
An even better option is to take the same bus mentioned above and ask to be dropped off at the market in Mae Chan. There are four scheduled services daily 07.30, 09.00, 11.00 and 13.00. The cost is THB60 and may involve a change in vehicle at the half way point, in which case the fare is THB30 as at December 2011.
From Tha Ton, there are yellow songthaews that go directly to Mae Salong. This also offers an alternative route for Chiang Rai and Mae Sai: coming back, take the yellow songthaew to the Tha Ton-Mae Chan road 30B, hop aboard a Tha Ton-Mae Chan green songthaew to Mae Chan another 30B, and then take the Chiang Rai-Mae Sai bus. This sounds complicated, but is probably faster than waiting for the "direct" songthaew to fill up.
For the return trip, both colors of songthaew hang out at the 7-11 in the centre of town. They stop running around 5 PM, but in a pinch or if in a hurry, the motorcycle cabbies can ferry you to Pasang for 300 baht.
By car
The shorter route is via highway 1089 from Mae Chan near Chiang Rai towards Tha Ton to Chiang Mai. The signposted turn off is next to a police station. From here travel about 13 km on some of the most amazingly curvy roads imaginable. The return trip to Mae Chan can be undertaken on routes no. 1234 and no. 1130 which wind through Yao and Akha hilltribe villages; you can also make a diversion north to visit the royal development projects and villas of Doi Tung.