By far the easiest way to get to Praga is to take the eastbound M2 Metro to Dworzec Wileński, and you'll be in the heart of the district. From Warszawa Centralna the 160 bus will take you across the river and drop you at the Park Praski stop, a great place to begin your tour of Praga. If you’re in the Old Town simply walk down the steps near the Royal Castle to Al. Solidarności and the Stare Miasto bus stop, taking buses 160 and 190 to head over the river to Park Praski. Trams 23 and 26 will get you to Praga and back from the Old Town area. These same buses/trams will return you to Stare Miasto.
You can also take a taxi which should cost around 20-30zł and should take you from the centre area to ul. Ząbkowska in less than 20 minutes. Please remember that the price and time depends on the traffic, so your journey may be longer during rush hours.