You can come to Kythera either by plane from Athens or by ship from Piraeus. You can also drive across Peloponnese and then come across from Gytheio or Neapolis by ship. During the summer months you can find flights from Thessaloniki and Seven Islands, too. There are ship itineraries from Crete, too.
For Schedules visit the link http://www.visitkythera.gr/en/travel/schedules.html
Municipality of Kythera +30 2736031213
Police Station +30 2736031206
Hospital +30 2736033203
Port Kapsali +30 2736031222
Port Diakofti +30 2736034222
Airport of Kythera +30 2736033297