With a US Passport, you can check-in online to avoid the 40€ surcharge. However, once you have printed your boarding pass at home, you need to get your boarding pass "stamped" by RyanAir at the airport in a process they call Visa Check (I believe it is true for all non-EU passports). In different airports, it works differently. But usually it is not at the ticket counter, but at a separate desk with a shorter line. The first time I flew them, I was not aware I needed to get the stamp and was stopped at security upon showing my boarding pass and told I had to go show my US passport and get the authorization. No big deal, as I was early. But worth keeping in mind since it does add time to the whole process.