Prague has one international airport – the Václav Havel Airport – located approximately 17 km northwest from the city centre.
To get to and from the airport it is best to use the public transport as taxis tend to be quite expensive mainly on this particular route. You can take BUS 119 to the Dejvická metro station (the green line) which takes about 24 minutes; BUS 100 to the Zličín metro station (the yellow line) which takes about 18 minutes; or the Airport Express to the Prague Main Train Station which takes about 35 minutes.
See http://www.prg.aero/en/ for more information.
There is another international airport in Brno which is mainly used by low-cost airlines. From Brno you can get to Prague by bus; the journey takes about 2,5 hours.
For more information see http://www.airport-brno.cz/index.php?id=0&lang=en.
Direct railways connect Prague with more than 20 European cities, including Munich (5 hour journey), Vienna (5 hour journey), Berlin (6 hour journey) and Paris (12 hour journey time).
The Czech Republic has one of the most extensive railway networks in Europe. You can reach almost every small town by a train and it can be a romantic way to travel around the country. The quickest way of travelling along the major lines is by express trains (called rychlík in Czech). Local passenger trains (in Czech osobní vlaky) make several stops along the way, but are very cheap.
For more information about schedules and prices see http://www.cd.cz/en/default.htm.
You can also get to Prague quite easily by bus. There are direct buses to all major European cities. Try for example Student Agency or Eurolines buses. International buses usually arrive at the Florenc bus station (also a metro station for both the red and the yellow line).