There is no airport on the island of Schinoussa and so you can only get there by ferry. Roughly said there is a ferry each day going somewhere (direction Amorgos or Naxos - Piraeus).
Some of the ferries arrive at Schinoussa at a late time in which case it is wise to make reservations on the island so you will be picked up in the port. You can check Blue Star Ferries and Nel Lines for their schedules.
In the Chora of Schinoussa there is a small village shop that sells ferry tickets just before the ferries depart.