If you are from the UK or an EU country you do not need a visa to go to Iceland for up to 30 days (Iceland has signed up to the Schengen agreement). This is true for some other countries including the US. if you are from a different area you can check your visa requirements here. You do need a valid passport and all the usual travel arrangements; and you should also be aware that the currency in Iceland is not the Euro but the Krona. You may get a better exchange rate in Iceland than at home though, so check this before you go. Most major credit cards are accepted.

You should also book some accommodation and check the weather! Iceland has an extreme climate and you need to be prepared. In midsummer the sun doesn't set for some weeks, while in the middle of winter the country is dark for most of the day. So you need to think what kind of trip you want and plan accordingly.

You can learn more about Iceland here.