Heimaey (The home island) is the largest and the only inhabited island of Vestmannaeyjar (Westman islands) achipelago. It is about 8 kilometers off the Icelandic mainland and you can quite easily reach it using the ferry going up to five times a day (usually) from Landeyjahöfn.
Most of the population lives in Vestmannaeyjabær.
How to find and get to Heimaey:
Heimaey is an island, so you have basically two options on how to come here.
The first and the most popular option is to come by ferry from Landeyjahöfn. The price is quite cheap (2.760 ISK round tripú. You can take your car with, not necessary, but if you plan to really go to discover the whole island, it can be pretty handy. Here is the Eimskip operator where you can make the booking.
The other option is to come by plane.
GPS coordinates of the Heimaey island: 63.442984, -20.270080 Take me there!