Attapeu is a town in Laos.
Buses leave from the Km 8 Southern bus station in Pakse. There are several buses per day but handy ones are 8am and 10am.
Green Paradise sells ticket from the island to Attapeu for a 120,000 kip (~14$). Every bus ticket shop on the island seems to offer the same price, line and company. A ticket should come with a boat ride that picks you up near the hostel you stay around 11am and brings you to Nakasang, where you need to walk 500m to the Green Paradise parking on the right side of the main road. After a first ride to Paksé, you'll be asked to change bus to another one that goes to Attapeu.
There appears to be nowhere to hire motorbikes in Attapeu (as of Jan 2014), although there is a possibility that you might get lucky asking one of the guesthouse if you can rent the personal motorbike of the owner. (Ex: The owners of Siamphone hotel rented their bike for 105,000 kip/day in March 2019)
Having one would greatly facilitate getting out and around so may be worth bringing one from Pakse - can be put on the bus or driven (200km).
Although you may find Tuk Tuk's at the bus station to greet buses generally there are no tuk tuks or jumbo's in town and you will have to walk everywhere (not such a huge problem as the place is kind-of small).
The major draw card of Attapeu would be Nong Faa lake out near the Vietnamese border. Access only in dry season and need 4WD or off-road motorbike.
Buses to Pakse (5 hours), Salavan and beyond depart from the main bus station at the edge of town as per the following schedule.
06:15 - Savannakhet
06:55 - Pakse
07:40 - Pakse
08:25 - Vientiane
09:00 - Pakse (VIP)
10:30 - Pakse
12:00 - Vientiane
13:30 - Pakse
15:00 - Vientiane (VIP sleeper)
16:00 - Vientiane (VIP sleeper)
To get to Salavan, you can also take one of the above Pakse bound buses and get off at Tataeng (40km south of Sekong) and wait for transport coming from Pakse or Sekong to take you the rest of the way to Salavan.