The bus fare from Olhao to Faro bus station is €3.25, the ticket seller at Olhao bus station cannot sell a ticket for the onward journey to the airport. The trip Olhao - Faro takes about 20-25mins. On arrival at Faro,  make your way to the new outside annex to the bus station, for the blue and white PROXIMO buses. Find the stop for the number 16 bus, usually there are tourists with suitcases queuing up. You buy the ticket on the bus, currently  €2.22. Cost all in all around €5.50 and say an hour and a half to be safe. The timetable says that the number 16 bus gets to the airport in 18 minutes. It does, once it gets going after the tourists have been sold their tickets. In total that saves around €20 on the taxi fare so quite a saving

Buses from Olhao to Faro are frequent on weekdays, say every 15-20 mins early in the day and stretching to half hourly later in the day.At weekends and on public holidays buses are much less frequent,with gaps of more than horu. Check the times for the day of travel at www.eva-bus.com

The number 16 to the airport rusn once or twice each hour from 5am to 11pm every day.  The timetable for the number 16 is here:
http://www.proximo.pt/pt/horarios/lin...

An alternative, and cheaper, is to get the train from Olhao station to Faro and walk the couple of hundred metres (at most) from the rail station to the stop opposite the bus garage.  Trains are cheaper and quicker than buses between Olhão and Faro, but are very irregular and infrequent, expecially at weekends.