By far the easiest way to get to Praga is to take the M2 Metro to Dworzec Wileński (eastbound to 'Trocka'), 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 stop, taking buses 160 and 190 or trams 3, 20, 23 and 26 to Park Praski. 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.