First I would like to say you one thing about Iceland's food: don't be scared! They don't eat anything odd, except for a few national foods which are not that usual: hákari (rotten shark meat) and hrutspungar (pickled ram testicles). These two are delicacies Icelanders eat for Þorramatur (a celebration held in February).
As almost every restaurant offers a carte in English, you can be pretty safe of what you will eat. Unless it is some soup, as soups are usually just súpa dagsins (soup of the day) or kjötsupa (meat soup). Enjoy them, Iceland's soups are pretty good, just a little bland (don't have a lot of salt, but are a little spicy).
The national fast food is the pylsur (or pylsa). It is a hot dog variant, with ketchup, sweet mustard, fresh and dried onion and remolaði, a mayonnaise-like sauce. The best place to eat them is in Bæjarins Beztu Pylsur (Best pylsurs of the city, in Icelandic) in Reykjavik, near the harbour and the flea market. It is definitely the best hot dog we have eaten ever, and ate quite a lot when we were at the capital. It can be found in gas stations all over the country, but better eaten in the best place!
I have tried to do something similar at home and the results were pretty decent, although the original is better. You can read more about my home-made pylsur recipe.
Dried fish is one of the other typical fast food here. We read in our travel guide that it is a typical snack while driving. I conceded and bought a pack of dried cod (once we realised which fish it was). If you like fish, you may find it interesting, but it was not that good. If you dislike fish... you better don't eat it. But it is worth a try nevertheless.
dairy product 100% Icelandic is skyr. It reminds of yoghurt, but I found it too sour. In fact, is a type of cheese, not yoghurt by preparation. I didn't really like it... until I found drykkur, which is a drinkable skyr preparation. It is available in several flavours (blueberries, peach and raspberries, papaya, strawberries and my favourite, vanilla), and can be found in almost all gas station supermarkets. Look in the fridges, it is worth the (usual) price of 250ISK.
smjör, butter. It is a very good butter. Slightly salty and creamy. You will find it everywhere for breakfast, and will probably forget you are eating a different kind of butter. Pay attention, it is different from the one you eat usually ;)
Another treat I loved was Frón's Póló chocolate and coconut cookies. You can buy them in some supermarkets (look for the cookies section and then for a blue tube with Póló written on it). If you like chocolate-coconut combinations, you'll love these cookies.