Arriving to Salvador by plane, your most economic way to get downtown would be by city bus.

Walk out of the airport, go straight ahead, cross 2 streets and by going around the fence keep your right and you will find a small bus stop.

Pick the one going to "Praca da Se" (R$2.80). It will take you toward the center square. You stay on until the end of the path Onibus. (Last stop) Count two hours in normal time, longuer in rush hours.

A slightly more expensive but sometimes more convenient option (especially for those arriving/departing late at night or early in the morning) is to use a pre-booked airport transfer. There are numerous companies online offering this service, such as Fox TransferViatorGreen Path Transfers and Grayline. Often the companies offer discounts at certain times of year and are of varying quality, so it’s best to shop around and read reviews from previous customers.