You will have to get to Tarifa from either Málaga or Seville airport. In both cases you have two options - to get there by bus or rent a car. The second way is still more convenient and faster.
So you can rent a car at Malaga airport here or rent a car directly at Seville airport here. There are several car rental companies at airports, so it's worth checking prices and conditions in advance.
If you want to take public transportation, you'll have to wait for a bus.
Malaga-Tarifa bus timetables: 07:30; 13:30.
Tarifa-Malaga bus timetable: 08:45; 15:45; 21:30.
Malaga-Tarifa bus ticket costs 16 EUR.
Sevilla-Tarifa bus timetables: 09:30; 14:00; 17:30; 20:00.
Tarifa-Sevilla bus timetable: 08:30; 12:30; 16:00; 17:00
Tarifa-Sevilla bus ticket costs 19 EUR.