Karpathos is quite a large island and there are many opportunities to get there. The majority of the connections are, of course, from Athens (flights are daily). You can get to Athens by cheap or regular airlines, or by other means of transport.
In the summer season, there are many direct connections from other countries. You can find them on Meltemi Windsurfing website.
On the southernmost part of the island, just next to Kastello climbing area, there is an airport – Karpathos International Airport (AOK). Flights to the island are mostly serviced by Aegean Airlines (aegeanair.com) and Sky Express (skyexpress.gr). There are several flights a day and they are relatively cheap. The simplest option is to get a direct flight from Athens. It’s worth looking for connections on these airlines websites directly because online travel agencies (OTA) may let you down. Every year, new connections appear from major European countries.
There are many connections available by European travel agencies. When choosing a charter, you can enjoy the advantage of a low price and a direct flight from your city. However, charters begin to be available during the summer season, that is from May to September. The offers depend on the country of departure.
Ferries to Karpathos run on regular basis throughout the year. You can easily buy tickets online (openseas.gr | ferries.gr) and come here from the Athenian port of Piraeus or all other larger Greek islands (Crete, Rhodes, etc.). Beautiful views are included in the price. The only disadvantage is a long journey (from Athens up to approx. 20 hours).
All of the above mentioned means of transport can be freely combined. There are plenty of possibilities, for example, a flight (charter or regular lines) to the island of Rhodes and a ferry to Karpathos.