Vientiane is the capital city of Laos.
North: Towards Vang Vieng / Luang Prabang
From the central bus station take a local bus to the outskirts of the city. Bus 23 goes to Tha Ngon for 5,000 kip ($0.65 USD) where is it possible to hitch and meet up with the main road north at Phonhong. Tha Ngon is around 25km north of Vientiane and the roads up there are small and easy to catch a ride.
Vientiane bus routes can be found on the official city bus website: http://vcsbe.com/routemap/ this lists prices, timetables and routes.
South / East: Towards Savannahket, Pakse, 4,000 Islands etc
To get to the south from Vientiane you will need to head East out of the city first as going south from Vientiane leads straight into Thailand. To catch a ride east, first take a bus from central bus station, number 14 goes to Buddha Park / Friendship bridge for 6,000 Kip ($0.75 USD). Get off somewhere on the main highway and begin to hitch once you are far enough out of the Vientiane suburbs.
East: Towards East: Towards Savannahket, Pakse, 4,000 Islands etc
To head east ask at the main bus station for a bus towards Dom Noun. There is kind a traffic circle right in the center of the town. It's a perfect sport to get a lift