The cheapest way from the Keflavík airport to Vakta is the Flybus. - Iceland Excursions/Flybus have buses from Keflavik Airport to Reykjavik Centrum Hotel at Adalstræti 16. It´s there where you get off the bus. Walk up Grjotagata and turn right on Gardastraeti. Vakta is the second house from the corner. See the map: https://goo.gl/maps/4R7Sj

The buses are always available in front of the airport building. You can also buy and book your transfer in advance. See the link: https://www.re.is/flybus/ One way ticket cost around 20 EUR per person. If you by return ticket as well, both ways will cost you 28 EUR.

Be aware, you have to change buses at the Bus station www.bsi.is and from there you get the bus to Reykjavik Centrum Hotel. You can also walk from the Bus station to Vakta. It will take you around 15 min.

The fastest way from the Airport is by taxi, around 40-45 min, but its more expensive. One way trip should be around 140 EUR, could be more, depending if its day time or night.