The answer
Take Próximo line 16 — the pink line — from the stop directly in front of the terminal to the Terminal Rodoviário in the city centre: €2.85 paid to the driver, cash or contactless, in about 15–20 minutes. It runs from 05:20 to 00:10, and the terminal is a 200 m walk from Faro's railway station.
There is no train at Faro airport and the 16 is the only bus into town, so it is also the cheapest way to reach the bus and rail stations for the rest of the Algarve.
Heading to a resort? Vamus Algarve's seasonal Aerobus (line 56) runs to Albufeira, Lagoa, Portimão and Lagos — check its dates before relying on it.
Two or more with luggage? A taxi is €12–20 for the 12–15 minute run, and Uber and Bolt both work at Faro.
⚠️ The traps (walk past these)
The fare is €2.85, not the €2.25 in older guides
Próximo's on-board line ticket is €2.85. The cheaper tickets do not cover this journey at all: €1.35 buys one zone and €2.00 buys two, and the airport is in zone 4 while the bus terminal is in zone 1, so the airport run needs the whole-line ticket.
Do this: ask the driver for the whole-line ticket to the Terminal Rodoviário and have €2.85 in cash or a contactless card ready
There is no train station at the airport
Faro's railway station is in the city, 6–7 km away, and the Algarve line is reached only after the bus ride. The 16 ends at the Terminal Rodoviário, 200 m from the station — turn left out of the bus station for the trains, right for the marina and the old town.
Do this: plan the 16 into any train connection and leave at least 20 minutes between bus and train
A bus signed Praia de Faro is going the wrong way
Line 16 runs both directions on the same stop: city centre ↔ airport ↔ Praia de Faro beach. Board the one signed towards the Terminal Rodoviário; the one signed Praia de Faro takes you out to the island instead.
Do this: read the destination on the front of the bus before you get on, and ignore the vehicle number
The last bus out of the airport is at 00:10
Line 16's last departure from the airport is 00:10, with a gap through the small hours until the first bus at 05:20. There is no night service and no rail alternative at that hour.
Do this: check the time against your landing, and use the taxi rank or an app if you are arriving after midnight