By bus
The main bus station is Mendolo, approximately 8 km to the east of the city center. There are regular services to and from Jakarta, mainly Sinar Jaya bus network, with costs around Rp 60,000 non A/C - Rp 75,000 A/C.
If you are planning to go to Wonosobo from Yogyakarta, you need to go to Giwangan Bus Terminal, and hop on to the bus to Magelang. It will cost you around Rp 15,000 depends on the bus, A/C or without A/C. In Magelang Bus Terminal, find a small bus to go to Wonosobo, the bus is without A/C. It will cost you around Rp 15,000.
You can get to the city center from Mendolo bus station using yellow Angkot. Just tell the driver to get to Plasa, the city center.
By car
There are several travel agents in Yogyakarta providing minivan Mitsubishi L300, Isuzu Panther to go to Wonosobo. the cost is Rp 36,000 - Rp 40,000.