You can come to Tinos by ship, departing from the port of Piraeus. It will take you roughly 5.5  hours. Speedboats departing from Piraeus arrive in about 3.5 hours, while boats from Rafina arrive in 2 to 4 hours, depending on the boat type.

Also, there are regular connections from Tinos to the other Cycladic islands, like Syros, Mykonos, Naxos, Paros, Andros etc.
For more information you can contact:

Port Authorities:
PIRAEUS 210 4226000
RAFINA 22940 22300
TINOS 22830 22348

Ship Line Agencies:
TINOS
Malliaris Panagiotis 22830 24241
Alimonos Yannis 22830 24301 - 22830 25716
Mariner 22830 23193 - 22830 24063
Markouizoy Athina 22830 22517

Ships depart daily both from Piraeus and Rafina.