If flying to Faro, I would recommend a taxi from the airport to the station, although there are frequent buses.
Around Faro itself, it is probably worth travelling on foot. Roads seem quite busy. To get further afield, I would recommend using the CP railway service. Fares are cheap and services fairly frequent. Trains run to places worth visting such as Lagos, Albufeira and Barreiro (for Lisbon).
Obviously most people fly to Faro. It has regular and chartered flights from everywhere in Northern Europe especially UK, Germany and Northern France. Scheduled flights also from Lisbon, Porto, London and German cities. The train from Lisbon is a scenic but slow ride. Long distance buses also run. From the airport you can get buses or taxis into the city. Faro train station is in the city centre.
The local bus service (yellow EVA buses) is efficient and cheap. Timetables are posted in Portuguese and English. Buses do not carry route (line) numbers as they do elsewhere in Europe. The network covers the local area and major towns but routes to inland towns are few and services relatively infrequent. Buses do not run after about 8pm in the evening even in the largest towns. Many routes only run every 2 - 3 hours at weekends. The bus company has a website with an interactive timetable at www.eva-bus.com. Beware going by bus to Albufeira - the new Bus station is a mile outside the town!
The local train service is limited to a single line along the coast. Local trains run every 1 - 2 hours. Between Faro and Portimao the stations are a long way from the towns they are named after! The train tends to go where the bus does not.
I don't drive so I depend on the buses and trains. If you plan properly you can get about to most places.
Unless you have a profound death-wish, do not even think about hiring a cycle. There are only two speeds for Portuguese drivers, fast and faster and add that to the hundreds of tourists in hire cars and you have the highest accident rate probably in Europe.
There is a train stop in Fuzeta. Train that goes all long the Algarve. But we prefer the car.
From Fuzeta we must take a small boat to go to the beach in the Armona Island. It's a very peasant 5 minute trip.
The best way to get there is by car. If You go from Lisbon You have a highway almost concluded until there. In the Algarve You have a highway crossing it all that connect the Atlantic to Spain. So, if You came from Spain You also can get the Algarve (and Faro) by car.
You can also take a plain to go to Algarve.
Faro Airport is 6 km away from Faro;
15 km from the Quinta do Lago;
20 km from Quarteira/Vilamoura;
30 km from Tavira;
35 km from Albufeira;
55 km from Portimão;
55 km from V.R.S. António;
70 km from Lagos.
If You have a boat, the marina is waiting for You.
Hire a car, if you can.
There is a dependable bus service right along the Algarve coast, but obviously this is slow because of the many stops.
A train service runs most of the length of the coast, but I have no practical experience of this.
1) By Car: If you hired a car you will have much more freedom and will be able to get there quickly. 2) By Bus: if you have no car or don't feel you would like to drive (you will miss many places). The Bus is not always a reliable transport ( it is either late or early according to the timetable or simply inexistent in certain days, like holidays and weekends). 3) By Train: make sure you take the Express Train especially if you are travelling from Lisbon to Faro ('Alfa-Intercidades'. 4) By Plane: Faro International Airport is only 10 Km away from downtown Faro.
Walking is the best way to get around. Other alternatives are to hiring a car or getting on the bus. Taxis will become a very expensive choice if you plan to do a lot of travelling. Warning: Taxi drivers might charge more than they should.