Hungarian Forint. Approx 308 HUF = 1 euro, 245 HUF = 1$.
There are exchange offices in all of the railway and bus stations in Budapest (and of couse also in the airport). You can also find many of them in the downtown. They change dollars, euros and nearly all of the major European currencies (NOK, CZK and so on).
Credit cards are accepted by ATM machines and in many of the shops. ATMs can be found in all of the major cities, but you can get into trouble if you look for them in a small village :)
Tipping is common (and somewhat 'expected') in Hungary. You should always give a tip in taxis and in restaurants. At most 10% will surely be enough, but in taxis it is satisfactory to round up the fare to the nearest hundred HUF.
Hungary is one of the cheaper countries in Central Europe, somewhat cheaper than the Czech Republic or Austria. Beer (0.5l): around 150 HUF, bread (1 kg): around 150 HUF, single bus/metro tickets in Budapest: 160-180 HUF (depending on where you buy it: at a station or from the bus driver), three day tourist ticket: 2600 HUF, weekly ticket: 3000 HUF.