Air
Eagle Air flies between Reykjavík and Höfn most days. Note that the airport is some distance outside the Höfn itself, so you'll have to figure out a way to get into town.
Bus
A bus from BSÍ bus terminal in Reykjavík leaves at 8:30am and gets in around 5pm, having stopped at many points of interest in southern Iceland. In the summer there is also a bus from Egilsstaðir, leaving at 1:30pm and getting to Höfn at 5pm. The bus stop in Höfn is the N1 gas station just off the main road leading into town.
Car
The Ring Road is the main road (and in places, the only road) through the entire Hornafjörður area, but Höfn is a few kilometers of the Ring Road is connected to it by road nr. 99. Höfn is a little over 450 km from Reykjavík and between 200 and 250 km from Egilsstaðir, depending on which route is taken
