Tinos is accessible by ferry from Athens or Mykonos.

We usually book through https://www.ferryhopper.com/

Athens:

The nearest port to the airport, and the quickest route to Tinos, is Rafina port. We recommend just getting an Uber or Taxi direct to this port. The quickest ferry from here is about 1.5 hours.

Alternatively, if you're exploring Athens or other Greek islands beforehand, you can also look at getting a ferry from Piraeus Port. You can take the metro to this port but ferries from here to Tinos take longer.

Mykonos:

There are direct flights to Mykonos from Luton and Gatwick on 1 October. From the island, its a short 30 minute ferry ride to Tinos.