There are numerous airlines going to Mykonos if you're not travelling on a "package holiday". Of course, there are all kinds of options if you've gone to a travel agent and booked a trip which includes your air and hotel, because then you're most likely to end up on a charter airline. But if you plan to get their on your own steam by air, here are some possibilities:
We went with German Wings from Cologne, Germany. German Wings has some great deals at good prices, and they fly to Mykonos from Cologne and also Berlin. Check out their website, www.germanwings.com
There are also about 5 flights per day between Mykonos and Athens with Olympic Airlines (www.olympicairlines.com), which run close to 100 Euros. The flight lasts 40 minutes. They also fly every day to Rhodes, a two hour flight, for about 90 Euros.
Aegean Airlines flies daily to not only Athens but also to Thessaloniki. Thessaloniki is a cool place and you can get there cheaply from Central Europe using Sky Europe. Websites are www.aegeanair.com and www.skyeurope.com).
To get to Crete, Santorini, or Rhodes, you can also go with Sky Express, www.skyexpress.gr
Lastly another great option is Air Berlin, that flies to Mykonos from Vienna, Nuremberg, Leipzig, Berlin, Hamburg, Hanover, and Duesseldorf. Website: www.airberlin.com
Mykonos airport (JMK) is served by regular daily flights from Athens by both Olympic and Agean Airlines, but also worth considering, especially during the summer, is direct charter flights from many European cities including Moscow and even from Tel Aviv. Finding a direct flight will depend on doing your own research from where you wish to fly but for an overview the site below has some (slightly out of date) information on the various airlines with direct services.
The airport at Mykonos is about 4km (10 mins) from Chora and has good bus links, hotel transfers or taxis.