Hellenic Seaways services Spetses several times a day from Piraeus all year-round (although times differ from summer to winter). Smaller, faster ferries take 90 minutes; larger vessels take between 2-3 hours. Compare prices and schedules and book here.
Alternately, it’s a 2.5-hour drive from Athens to the port of Kosta (near Porto Heli). From here, you can catch a 10-minute water taxi to Spetses for about €20 per boat.
To find out more about Spetses, visit here.