Roads to the north are sealed, while the southern part to Shangrila is rubble and dirt, currently under reconstruction.
By bus
The Bus Station is at the southern end of town. The ticket-office is through the side-entrance of the building on your right hand side when facing uphill. Be sure to buy your advance-ticket on arrival, because buses can get crowded in summer. In low season it's ok to buy your ticket just before you leave, but the ticket office opens very shirt time before the bus leaves, especially in the morning. Buses arrive from Shangrila 6-9 hours, 85 yuan, departs daily at 8:00, Kangding 12-14 hours, ~160 yuan, departs daily at 6:00.
Departure times are as of November 2007 and both buses tend to leave earlier and fill up quickly! It is not possible to buy tickets to Litang currently though the Kangding bus will pass through. If you want to go to Litang you have to share a minivan or taxi for about 400 yuan per vehicle. It's a scenic 4-5 hour ride. You'll find them near the central square on the main road through town. Alternatively position yourself at the main road near the bus station, you should be able to find a car to join. Locals travel early though, be around when the buses are leaving - 6am!
Update 04/04/2012: Shangri-la bus station is currently not selling tickets to foreigners for Xiangcheng, due to a ban on foreigners in the region. Apparently there are road blocks where police will turn away foreigners trying to get in to Ganzi province.