From the central Bus station you will have to walk the Ante Starcevića until there is a really big cross (1km). Then you turn right on to the Jadranska cesta. This road is heading to Šibenik and Split. After 200m you will find a busstop where you can place yourself. It is not recommended to hitchhike the motorway, because there is not so much traffic (peage) and the landscape on the coastroad is much more beautiful.
The street is named Zagrebačka ulica and can be easily reached by walking straight up East (leaving the sea behind) from the main bus station on Anta Starcevića or taking busses 4 or 6 from there (be sure you get into the one going the right direction! There are two bus stops on the same side of the street across the bus station, and you want the one on the East side; when not sure, ask the driver if they are going towards Supernova shopping mall, otherwise you might end up taking a long tour around Zadar). For bus 6, you want to get out at Supernova and go back to the main road (just on the side of the mall), there is a bus stop there. For bus 4, get out at Crno (the first stop when it goes out of the Zagrebačka) and get back to the road, there is a bus stop, as well. No shade, so have water to survive Balkanian summer heat.
The main highway starts about 10 km away, therefore if someone offers to take you there, it's best to agree. From there, if you want to go to Zagreb, go to the peage (cestarina). There are two ways to Rijeka, one of them is the same highway, the other is along the coast. Tomasmarc stayed at the crossing between the peage and the coastal road with a sign "Rijeka" (to get the best of both) and got a lift pretty fast.
There is a youth hostel in the very north of the town. The district is called Puntaminka. From the center it is a 40 minutes walk. But you can even try to hitchhike. It costs app. 12€ (90 Kuna) per night.
Please DON'T do it south of the city, there are areas left which are contaminated with landmines.