From the South Airport you can take buses to Playa de Las Americas (routes 111 and 343). The fare is about 2 EUR, travel time - 45 minutes). Buses #340, 343 go to Playa de las Americas from Tenerife Norte. On average, the fare for public transportation will be 2 EUR and the travel time is about 45 minutes. Also from Tenerife Norte you can take buses №101, 102, 107, 108 to Santa Cruz, and then - №111, 112 to Playa de las Americas (about 10 EUR one-way). Upon arrival, it is recommended to purchase a Bono Bus card, which allows you to save up to 50% on travel.
If you want to get to your destination a little faster, you can use cab services. Thus, a trip from Tenerife South Airport to Playa de las Americas will cost 25-35 EUR (+25% after 22:00 and on weekends), from Tenerife Norte - about 80 EUR if booked in advance, up to 100 EUR without booking (the tariff outside the city is a little more than 1 EUR per 1 km). There is a single fare for all cabs and payment is strictly by meter. There is no need to order a cab in advance, as there are always free ones at the South Airport parking lot.