There are mostly three ways to drive into ÃsafjÃ¶rÃ°ur. The first is from the ringroad in HrutafjÃ¶rÃ°ur, and goes up north on the eastern part of the peninsula through road number 61. That way gives you the opportunity to stop in Holmavik among other places on the way.
The second way to get to ÃsafjÃ¶rÃ°ur by car is by road 60 from the ringroad, 608 over the moor of Thorskafjardarheidi and then 61 through the many fjords on the way. In the summer, that is the shortest way from Reykjavik, but it is currently not accessible during wintertime.
Thirdly, you can take the ferry Baldur from Stykkisholmur via the small towns on the western part of the peninsula. That way gives you a chance to see for example the great waterfall Dynjandi.
There are regular busses that go from June 1st to 31st August from Akureyri and Reykjavik. Information on that can be found on West Tours' homepage (http://westtours.is/index...)
Additionally, there are two daily flights from Reykjavik with Air Iceland. The fare is relatively cheap if you just want to go from A to B, and you are treated to a grand view of the fjords on the descent into the ÃsafjÃ¶rÃ°ur airport. The airport is about 5 km from the town, on the other side of the fjord. It's possible to walk from the airport to the town if you don't mind walking on the gravelled shoulder of a lightly-trafficked road.