You can book a safari at most of the hotel receptions or local travel agencies. It's hard to miss the publicity as the safaris are a very popular activity in the Algarve.
There are several companies that make the tours all around the Algarve. You can choose from Monchique to the rural Algarve, Sagres (the very eastern end of the Algarve) to Spain. Prices may vary according to the length of the tour. Normally they are one-day tours, but special night tours or three-day tours are also available.