If you decide to go down the public transport route, you should consider buying a ticket that is valid for several days. That way, you not only save money, you are also 'done' with it for the rest of your stay. Unfortunately, at the airport, you can only buy tickets valid for 3 days (72h) or less. If you are after a longer duration, you need to fill out quite some paperwork, but that is material for another article. The 72h ticket is valid for you, your luggage and you can use all Prague buses, trams, metros, the funicular and the cute little passenger ferries over the river with it. Just stamp (validate) it when you board the bus for the first time and keep it with you in case of being controlled. For the duration of your ticket, you can now jump in and out of Prague's public transport as often as you like.
Where to Buy your Public Transport Ticket
From 07:00 to 22:00 hours you can buy a ticket from one of the official Prague public transport counters in each of the arrival halls. Outside these hours, you can buy your ticket from vending machines at the bus stop (you will need Czech coins for that!) or directly from the driver (slightly more expensive, but he will accept notes / bills also, but again, only in Czech Crowns).
Where to find the Bus to Prague
As Terminal One and Two are so close together, the bus stops are just in front of you, just go out through the main door, straight ahead, passing the taxis, and you hit the public transport terminal. To find the right bus, simply look at the numbers displayed at the stops.
The most common situation now will be to take the airport bus (119) to Dejvická and then continue your travel with the tram and / or metro to your end destination, as most tourist accommodation is in, or close to, the center of Prague. Ask your hotel or hostel about the nearest tram, bus or metro stop and use the DPP website, link and explanation below, to find your connections. There are several bus lines that leave Prague Airport and go towards the city, the two most frequent variations are below:
Dejvická: As already mentioned, here is where the normal airport bus ends (119 being the daytime bus, 510 the night bus) and from here you can enter the metro system, green or A line, which goes directly to the center of Prague and beyond. As for trams, the number 20 and 26 (day) and 51 (night) trams depart from the same place, whilst around the corner (5min walk, take the underpass through the metro / subway / underground area) you'll find also the trams 2 and 8. A bit further down, from where you left the airport bus, you'll find a major bus stop from where a variety of buses depart, most of them towards the suburbs, so normally not of great interest to you.
Zličin: Bus 100 will bring you to the beginning of the yellow, or B metro line which in turn, goes towards Andel (Anděl) a major tram and bus hub in the south-west of Prague city center.
If all this sounds like 'Bohemian Villages' to you, like we say in German, have a look at the DPP website!