There are three major companies that offer airport transfers. Flybus, Airport Direct and GrayLine.
The most common and best way for small groups (1-4 persons) is the FlyBus+. It is a large bus with up to 60 persons. If you have your ticket with you, you can go directly to the bus outside the Arrival hall of the Airport.
The nearest drop off location is Bus stop 12 – Höfðatorg, it is located in front of Foss Hotel Reykjavík, only about 2 min walk from the apartment.