Become a citizen of the EU country whose passport you'd like to get. Becoming a citizen is not easy. Typically, you have to live legally in the country for a prolonged period of time, be born in the country, marry a citizen of that country or have a proven direct family link with somebody who had been a citizen of the country.
Apply for a passport. Passport applications differ from country to country. However, they generally require a completed and signed passport application form, two photos, documents proving citizenship and a fee. In addition, some countries require a guarantor to co-sign your application. A guarantor is a practitioner of a widely respected profession, for example a priest or a university professor.
Get your passport via mail or pick it up yourself at a relevant government office. Passport delivery takes about two to six weeks, though many countries allow a fast-track application, in which you can pick up your passport within 24 hours of handing in your application.
