You can explore Yogya on foot around the Malioboro area - which is the main shopping street. However, traffic is heavy with hundreds of bicycles, trishaws & cars. If you are staying for a few days, it is advisable to hire a car with a driver who can drive you anywhere in the city & to the historical sights. Most car hire fees include petrol. Meals fee for driver and tipping are optional, but expected. You can easily book a car with your hotel or car rental companies (some can be booked in advance). 

Becaks (Trishaws) 

Wherever you wander on foot in Jogja, you can be guaranteed to hear the familiar, "Becak, mister?" from one of the dozens of becak-drivers. A becak is, basically, a modified bicycle with a twin seat on the front, with the guy on the back. pedalling. Good if you want to experience a more open and leisurely view of the town, but not so good if you like to breathe in the copious amounts of pollution given off by other traffic.

Beware: Becak driver that operates around Malioboro area tends to deviate guest's plan. A simple example is that some drivers will told you a particular attraction is closed for the day and instead take you to shop at their partner shop. This way, the becak driver will get commission from the shop and you will loose your precious time to miss the attraction. It is advisable to know where you want to go (don't just ask the driver to bring you around, but tell the driver your intended place) and decline if the driver offer you to shop for souvenirs. 

Andong (horse-carriage)

"Andong" or "Delman" is another popular mode of transport to be found in Malioboro area. As like becak, you have to deal with the driver on your destination first before embarking. Delman has larger capacity than becak - typically can fit 4 normal adults conveniently. Hence, it's a preferred way to explore the city center with family and friends. 

Scooters

Scooters have been found for hire for as little as Rp 18,000 ($2US) per day in the tourist-area of Jogja, around Prawirotaman, but you need to provide your own gas for these, and might be an idea to get them checked over at one of the many Honda service-centers dotted around the city, just to make sure you last the day on one of these. You often take your life in your own hands when you brave the traffic on the streets of Jogja!

TransJogja bus system

TransJogja is a special bus system in Yogyakarta. The bus ply certain routes and only make stop at designated bus shelters. As of October 2010, there are 4 sets of route of TransJogja; 1A, 1B, 2A, 2B, 3A, 3B, 4A, and 4B. Basically, each set ply the same routes, only differ in direction. Also, as some of the roads are one-way, not all "A" and "B" bus stop at the same stretch of road. For visitors staying around Malioboro area, "A" bus (with exception of route 4A) ply the route but not "B". 

Single journey ticket is Rp3,000 with operational hour between 0600 to 2200 (6am to 10pm). You can read more about TransJogja here  (website in Bahasa Indonesia, you can use free translator).

Public buses

As in other cities in Indonesia, public buses are rather inconvenient to take. It is cheap but it will be confusing and time consuming. Most buses will terminate at Yogyakarta's 2 main bus terminal: Jombor and Giwangan. Normally when you embark the public bus, you pay the fare directly to the bus assistant (or "kenek" - read: "kuh-neck" in Indonesian). If you are not a regular, sometimes the bus assistant will cheat you on the fare to pay as there is no printed info on the bus fare. 

Taxis

Taxis are aplenty and can be easily booked on the phone or hailed by the streets. Different taxi company has different fleet colour so it's easy to recognize your preferred taxi company.