The small island of Tinos is part of the Cyclades Islands, the same cluster that is home to Santorini and Mykonos. If you're coming from Athens, head to the port of Piraeus and take the ferry to Tinos, which takes as little as 2 hours.
There is also the option of taking a taxi to the port town of Rafina and ferrying over from there, but the traffic is often terrible from Athens and can double the driving time. That said, the journey from Rafina to Tinos is a short 1-hour and 40-minute ferry ride, so it's convenient if you're already in the port town.
You can also get from Athens to Tinos by switching transportation in Mykonos. Fly from Athens to Mykonos, and then from there take a short ferry ride to Tinos. If you're visiting one of the other islands in the Cyclades, like Santorini or Syros, there will very likely be a ferry to Tinos available.
Additionally, there's always the option of taking a tour: take this 10-day trip that starts in Athens, weaves through Naxos, Mykonos, and Tinos, then loops back to finish in Athens.
Duration: 2.5-3 hours
The fastest and most convenient way to get from Athens to Tinos is by taking the ferry from Piraeus, Athen's main port. Select from one of the many ferry operators departing for Tinos, the quickest route taking 2 hours and 45 minutes to get to Tinos Ferry Terminal.
Another option is flying from Athens to Mykonos, then taking a ferry to Tinos. The M3 metro gets you from the city center of Athens to Athens International Airport Eleftherios Venizelos (ATH) in 40-45 minutes. Take a flight from there to Mykonos International Airport (JMK) which takes as little as 35 minutes. Keep in mind that you should arrive 90 minutes before your departure time.
Upon arriving in Mykonos, take a 10-minute taxi to the Port Authority Coastguard and hop on a 20-minute ferry operated by SeaJets to Tinos Ferry Terminal. You can buy the tickets in advance online, and be sure to check the schedule because ferries only run once a day.
From the Cyclades
Duration: 20 minutes to 1.5 hours (depending on the island)
As mentioned above, you can ferry from Mykonos to Tinos in a short 20 minutes. In the case of Santorini, head to Santorini Athinios Hafen—Santorini's main port—and take the ferry operated by Starjets to Mykonos, and then transfer there to a ferry at Port Authority Coastguard that's headed for Tinos. Again, keep in mind that these ferries only run once a day, so be sure to check the daily schedule.
Other popular islands in the Cyclades cluster that have ferry routes to Tinos include Paros (1 hour and 25 minutes), Naxos (1 hour and 20 minutes), and Syros (45 minutes), to name a few.
Duration: 1 hour and 40 minutes
From the port town of Rafina, you can easily take a ferry from Rafina Port Authority to Tinos Ferry Terminal, which is a 1-hour and 40-minute journey. It's good to note that ferries only run once a day at 7:40 a.m., so plan your trip accordingly.