By Bus: Iceland’s local transport is limited to bus and taxi. Iceland has an extensive network of long distance buses that run to most of the places including Reykjavík,  Akranes, Borgarnes, Hveragerði, Selfoss, Hvalfjarðarsveit, most places on the Ring Road, popular hiking areas, and Snæfellsnes Peninsulas.
Therefore, the best public transport to commute around Iceland is a bus. You can book online or get bus passports to travel. The bus passports are offered every summer when the tourist season is at peak for the convenience of the tourists.
By Taxi: Taxi is another option you can consider while commuting around Iceland. Taxis operate in Reykjavík area and many other larger towns. Although they are metered, they can be pricey and it is always wise to prebook.
By Car and Motorcycle: The roads are good and the traffic is light which means you can easily get around in a rented car or motorcycle. It is a great deal if you are travelling in a group of 3 or 4 but again the gas is expensive in Iceland.
By Train: There is no train network in Iceland.
By Boat: Some ferries operate around Iceland and takes you from Bolungarvík and Ísafjörður to points in Hornstrandir (Westfjords)