Due to the political problems between Iran & USA governments, the visa application process for US citizens differs from other nationalities.
You need to know that the visa authorization is required before your arrival in Iran. Normally it takes 10 working days for the rest of nationalities but it can take up to three months for US citizens. The MFA of Iran has to evaluate your documents and approve your Itinerary which can't be changed once you proceed for the visa.
Once you receive the visa authorization number, you can purchase your tickets to Iran and collect your visa on arrival.
American citizens such as Canadians and English, unlike other nationalities, must be accompanied by a local guide and, as we mentioned before, they have to follow the strict itinerary.
The only place in Iran, that tourists can visit without visa, is Kish island located in Persian Gulf. You can stay in this beautiful island up to 2 weeks.
You can apply for your visa on our website: https://goo.gl/gw5NUd
Related: Visa information