Travel to Kalymnos
Fly to Kalymnos Island.
This is the most convenient way to come to Kalymnos.
Fly to Kos Island.
This is the best next option and the cheapest one.
Come from other ports.
Kalymnos Island is connected by ferry with other islands and Piraeus, the port of Athens.
To see which are these islands, check the links saying "other ports".