How I did it: I used 'Teach Yourself Icelandic', and I also picked up an English/Icelandic dictionary.
I found it easy to get started but difficult to progress. I mastered a few chapters of the book but I found I would get stuck going over the same chapter over and over again and not taking in any more information.
I went to Iceland with a basic vocabulary and some difficulties with pronounciation, and I came back feeling much more confident with the language. Immersion is certainly the best way to learn, and I think if I had spent more time there I would have learnt more quite quickly. Read how I did it… 5 years ago