My journey to learn Icelandic has been fun, frustrating, and all types of emotions in between. I still tell people that I am working on being fluent because I don’t want to be held responsible for any terrible mistakes that I am bound to make.
Pronunciation of Icelandic like a native speaker is by far one of the tougher parts of the language. Of course, declining of words is harder but I think pronunciation is a close second. The one thing that helped me the most with pronouncing Icelandic words as close to native speaking as possible was to ask a native speaker to constantly correct me when I spoke.
When I was married to Gunnar, he was the person correcting me the most but I also asked my co-workers and friends because I was determined to get it right. Doing this can cause a lot of frustration because there are sounds in Icelandic that might be foreign to your mouth or mother tongue. I also think listening to a lot of Icelandic helps too but the key is to have a teacher or friend who speaks Icelandic well to help you.
It is also helpful to know that some people speak Icelandic with an accent. Meaning, they don’t sound like a native speaker when they talk the language but what they are saying is correct. That is totally fine and there is no reason to beat yourself up because you don’t sound Icelandic.
However, your question was mainly about pronunciation so I am addressing that. I am still a stickler with how I say things even to the point where I am over pronouncing words and I am learning to say things more colloquially. The more you learn Icelandic, the more you will hear that Icelanders don’t always pronounce every part of the word. That can cause some confusion at times but with practice and a trained ear, you will pick up on it.
If you don’t already, I would look into private lessons with an Icelandic teacher to work on your pronunciation, if you don’t already have one. iTalki is one place that has teachers. Also, there is Icelandic Made Eas(ier) by Siggi. Lastly, there is a great app called LingQ, where you can hear and read in Icelandic from different sources online, like videos, songs, and so on. It is awesome and the premium version is totally free for those learning Icelandic.
Viltu læra íslensku? and Íslenska fyrir alla are other resources for learning Icelandic and hearing it spoken.