From the airport to the capital Reykjavík
From the international airport Keflavík to Reykjavík is easy to catch the "Flybus" (ca. 45 min.) but you could of course rent a car, i.e. from Europcar which has an office located at the airport in Keflavík and in Reykjavík.
The Landsmót grounds
The competition grounds in Reykjavík are called "Víđidalur" and it is located in the suburb of Reykjavík. For your Google Maps App, type "Brekknaás 5". For further information, let this map help you.