Flying:
If you want to fly up north there are two domestic airline companies that offer scheduled flights, to Akureyri and Húsavik.
Akureyri airport keeps track of all flights from and to Akureyri you can see the list here www.akureyriairport.is.
To Akureyri:
Check the domestic airline Icelandair, www.icelandair.com
Icelandair flies out of Reykjavik to Akureyri in the north. With several departures every day, check their homepage for the schedule.
Keflavík connection:
Icelandair connects with Icelandair flights via Keflavík International airport, more information here https://www.icelandair.com/flights/campaign/keflavik-akureyri/
To Húsavik:
Eagle air flies out of Reykjavik to the whale watching capital Husavik. Several departures every week, check their homepage for schedule. www.eagleair.is
Driving:
By bus:
Strætó bs. operates 7 days a week all year, with exceptions on holidays . The distance from Reykjavik to Akureyri is 380km, and the trip takes about 6 1/2 hrs. For further information and schedule check their homepage at www.straeto.is.
By car:
Renting a car and driving yourself is another possibility. The Ring Road no. 1, goes around the island and is mostly asphalted two-lane road. While traveling the Arctic Coast Way you will have parts that are gravel and narrow. Check the homepage of the road administrator at www.vegagerdin.is for the distances and condition of the roads.
Read more here about driving on the Arctic Coast Way.
If you are coming from Europe it is possible to bring your own vehicle with the ferry Smyril line. The ferry sails from Denmark via Faroe Islands to Seyðisfjörður on the east coast of Iceland. For further information check www.smyril-line.dk