By far the easiest way to get to Praga is to take the M2 Metro to the end of the line (Dworzec Wileński), and you're 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 (you can nod at the bears as you disembark). 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 and buses 160, 190 and 527 head over the river to Park Praski as well. These same buses will return you to Stare Miasto as well. Trams 23 and 26 will get you to Praga and back from the Old Town area.
You can also take a taxi which should cost around 20-30zł and should take you from the centre area to 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.