The adjacent bus and train stations are about 15 minutes walk from city centre. There are frequent buses and taxis too.
Frequent buses run to and from Zagreb (3h 30 min), Rijeka (change for Trieste in Italy), Pula, Sibenik, Split and on to Dubrovnik. Information: +385-23-211555. Reservations by phone are possible with some operators, e.g. Contus: +385-23-314477. Touring connects Zadar with several German cities.
About half the buses for Zagreb pass through the stunning Plitvice National Park.
Large Jadrolinja http://www.jandrolinija.hr ferries run every few days up and down the coast between Dubrovnik and Rijeka, stopping off at ports (including Zadar) and islands on the way. They also run almost daily ferries in summer to and from Ancona in Italy.
There is an evening flight from Zagreb. During the summer seasons there are also various tourist flights from several European cities. Cheap flights exist but may be hard to find. AdriaJet  sells tickets on charter flights: tel. +385 48 240600. Ryanair  has added a low cost flight from London Stansted to Zadar.
The centre is easy enough to get around on foot. To reach the bus & train stations or Youth Hostel you will probably need to catch one of the frequent local buses.
Sit for hours in one of the cafes and enjoy the city, the sun, and the people. There's very few Internet Cafes. For more information visit the tourist office at 
If you are looking for a good printed tourist guide try the Petar Zoranic bookstore, Knezova Subica Bribirskih 10