Turkey has excellent connections to Europe and the world, especially through Istanbul, its major city where you can travel from many different countries for quite low prices.
Turkish Airlines (THY) is the national airlines of Turkey and they have regular flights to Istanbul from principal capitals and major cities of the world for very reasonable prices. For example you can easily travel (2-way) to Istanbul from Amsterdam, Berlin, Dublin, Frankfurt, London, Paris and many other European (especially German) cities for 150 to 250 EUR. Also, round trip flights from USA (New York, Washington, Chicago, Los Angeles and Houston) are in the price range of 400 – 700 EUR.
There are two international airports in Istanbul: Ataturk airport, the bigger one, is in European side and most of the international flights are conducted through it. However, this airport is further away from most happenings and services in the city of Istanbul.
Sabiha Gokcen Airport is in Asian side, it is newer but smaller than Ataturk Airport. However, THY also runs international flights from Sabiha Gokcen as well, but these are less frequent.
Please check out http://www.thy.com/en-INT/index.aspx for detailed information.
Another airline company, Pegasus (PGS), operates in Turkey and it conducts international flights from different countries to Sabiha Gokcen Airport. You can use PGS to reach Istanbul from London, Paris, Brussels, Zurich and many Italian and German cities. Please check out http://www.flypgs.com/en/ for detailed information.
OTHER MEANS OF ARRIVAL
The best way to reach Turkey is certainly by plane, but there are also regular ferries from Italy and Greece to Turkish Mediterranean ports (Izmir, Antalaya, Marmaris) from May to October. In the same period, there are a lot of Mediterranean cruises that include visiting Turkey, so if you can combine your holiday with your dental care, it might be a great option.
Traveling by car, bus or train only makes sense for shorter trips, coming from neighboring countries, but even then the plane ticket from Athens to Istanbul is cheaper than going by car, and much faster than using train or bus. However, if you are feeling the adventurous spirit of exploring Turkey and the Balkan countries, you can take the Istanbul Express train from Munich, through Slovenia, Croatia, Serbia and Bulgaria, to Istanbul.