Icelandic consulates nowadays do not issue visas, therefore you need to contact a Danish embassy near you. Make an appointment in advance with a local embassy official there. Also note that you cannot apply by post, so best get in touch with them by email or phone.
Tourists visiting only one Schengen country can apply to the respective consulate. However, those tourists visiting other countries on the same trip will have to apply to the consulate of the main destination country or the one they will enter first - in case there is no main destination.
US tourists are encouraged to enroll in STEP program (Smart Travelers Enrollment Program) at the embassy. This facilitates easy communication on your trip or visit. It helps the embassy to keep you updated on important security announcements and safety announcements. Moreover, your family and friends can easily get in touch with you in case of an emergency.
As per the Schengen agreement, citizens from the US, Canada, Japan and Australia can stay or visit the country for a period not exceeding 90 days or 3 months without a visa. Exceeding that, one will need a visa to continue staying in the country for tourist purpose or business reasons.
In addition, one needs to show that they have sufficient funds and a return ticket to continue staying in the country. The validity of the national ID or passport must be at least 3 months beyond proposed stay period. However, nationals from Australia, Japan, Canada and the US will need to have a return ticket.
Holders of diplomatic service and passports are exempt from obtaining a visa for Iceland. In addition, stateless persons and recognized refugees living in an EU country and have travel documents from that country are also exempt from visa.
Other exemptions include students requiring visa to travel to Iceland, but reside in an EU country which applies the EU decision 94/795/JHA of 30th November 1994. This is only if they are traveling with their school teacher.
A visa application for Iceland can be obtained from the nearest embassy. For a complete visa application, one must have a filled out visa application form, a valid national passport, two passport photographs, confirmation of health insurance, proof of hotel booking and airline reservations, a current bank statement, and possibly a reference letter through your education or employer, plus the visa processing fee.
Schengen visas are only for temporary visitors who do not intend to stay for long. If you intend to stay for more than 3 months, you will need a separate visa issued from the Danish embassy for Iceland. Make an advance application. Processing of these visas can easily take 15 days from its received date at the embassy. In some circumstances, the wait time can go up to 60 days.
In case there is no Icelandic or Danish embassy in your country, you can contact the embassy of a neighboring country such as Sweden, Norway, Germany or France.