At Faro Airport you there are lots of car hire companies. Do a search on the internet to find one that you are happy with.
Alternatively you can use the one that we use. The one which the family uses regulary is Auto Season Rent a Car.Simply e-mail them with your dates, flight details and the type of car you want. They will e-mail back and if you are happy confirm. The detail are below if you wish to use them.
tel: 281 957 327
address: Lot. Irmaos Luis Bote, Loja 2E, 8950Algoa-Altura
On arrival at Faro there will be number of Car Rental companies displaying names.
Find your name on one of the boards. Complete the paperwork and thats it.
A nice touch is that after the first visit they keep your details which makes renting a car very quick thereafter.
On your return you simply leave the car in Car Park 4 with the keys in it. Walk away and go to check in. It really could not be simpler.