From the airport you can easily transport yourself to the central part of the city via taxi, bus or train. Tickets for the train are preferably purchased in ticket machines or ticket booths at the airport, but it is very important to validate the ticket before entering the train.
Controls are quite common on the trains and buses and non-validated tickets results in rather stiff fines. Also remember to keep your ticket all the way until you have exited the station. Controls are also conducted inside the stations before exiting.
The same goes for travelling by trolley or bus - make sure to validate your ticket when boarding and keep it until you have exited.