Getting around Buda & Pest is easy with the Metro system they have... You have 3 choices, Underground Sub, An above ground Tram or the Busses...
We purchased a 3 Day tourist card & loved that we could hop around town without having to stop & purchased anything else...
You can purchase a 1, 3 or 7 day tourist cards, They are only good for the BudaPest area, so if you are taking a day trip, You'll have to purchased an AddOn.