How to get to Patmos
There are many ways to come in Patmos, the easiest is to come with Blue Star Ferries or Hellenic Seaways from Peiraias port. Scheduled routes for summer are 4 to 5 days per week and the trip takes from 7 to 8 hours. You can use TravelPlanet24 to find the most suitable ship for you.
Patmos does not have an airport so if you want to come by plane you should fly to Kos, Rodos, Samos or Leros (recommended) and get the local ship Catamaran. There are routes every day. There is also the flying dolphin from Samos or Kos.
And finally if there is no ferry or plane that suits to your needs you can swim from Piraeus port, assuming that you swim with 2 miles per hour and Patmos is 166 miles from Piraeus you will need about 3 and a half days!!! :P