As the state is not recognised by any international organisation, its Ercan Airport is not recognised by the IATA. This means all flights (including charters) must touch down in Turkey before continuing to Ercan. Scheduled flights on Turkish Airlines, Atlasjet, Pegasus and Onur Air connect via various destinations in Turkey, and to countries such as the UK, Germany and Iran.
It is also possible to fly to airports in southern Cyprus (Larnaca is the closest) and take a taxi to the north, crossing the Green Line near Nicosia. Greek Cypriot taxi drivers may not be willing to take tourists to the north. See details on crossing the Green Line below.
When passing a Green Line checkpoint between the Republic and TRNC or entering via air or sea, TRNC immigration will stamp either a piece of paper (which seems to be the norm at the Green Line) or your passport (which seems to be the norm at air and seaports). You can usually get the officer to stamp the other document if you so wish. As TRNC stamps are no longer a problem for later visits to Greece or Cyprus, at least for EU citizens, you may choose whether to have that souvenir stamp in your passport or not.
One uncertain source told that you can only get 1-day visit "VISA" if you enter Northern Cyprus from Cyprus-side but this may be wrong or may have changed.
Beware that if you are not a European citizen and you enter the island at the north, the officials in the south may deny you the entry, though there have been reports that this rule is not strictly implemented, especially for Canadian and US citizens. For European citizen, entry to both sides constitutes no problem.
EU citizens can cross at any of the border crossing points, the main ones being in Nicosia. The Ledra Street crossing is pedestrians-only but the crossing slightly further west, at the old Ledra Palace Hotel (now used as the headquarters of the UN peace-keeping force) seems to be used for cars as well. EU citizens are given a separate paper as a visa, and this is valid for 3 months and can be used as often as you like, so it is possible to wander between south and north Nicosia at will, providing you are prepared to queue up to get your visa stamped each time. This was certainly the situation in late December 2013