Santorini (Thira) Airport: There is no direct rail or metro; the budget route is KTEL bus to Fira, then the Fira–Oia bus. Allow roughly 75–120 minutes including the connection, and carry cash and small change; fares are low but timetables are not built around every flight. For arrivals with luggage, late flights, or a fixed check-in, use a pre-booked transfer/direct taxi to Oia: roughly 30–40 minutes in normal traffic. Do not pay for a vague airport “tour” transfer when a plain point-to-point transfer is what you need.
Athinios Ferry Port: Take the port bus to Fira and change for Oia; allow about 90 minutes to two hours once ferry unloading, queues and the connection are included. It is cheap and cash-oriented, but miserable with substantial luggage in summer. A pre-booked taxi/transfer is the sensible splurge after a ferry; the road to Oia via Fira is winding and traffic-prone. Wikivoyage quotes port taxis at about €20 per group, or €25 for a non-shared ride, but treat that as an old rough benchmark rather than a guaranteed current fare.