Visit or call the embassy near your residence and arrange for an appointment. This is the only way they will accept an application.
All Schengen countries are in Europe. However, it should not be confused with the European Union (EU). The 24 Schengen countries are: Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain and Sweden. Schengen and EU are two different types of agreements between European countries.
A Schengen Visa allows the holder to travel freely within all of the Schengen countries for an extended period of 180 days; however, one country must be stated on the application even if you are making multiple stops. Once Schengen is in hand, you can then apply for legal residence and stay after 180 days.
Be sure to obtain your visa well in advance of your departure from the U.S. It is not unusual for an application to take a long time depending on the type of visa required. Your passport must be valid with blank visa pages in order to apply for a Schengen visa to a specific member country.
Check with the specific country's consulate as various types of documents are needed to be compiled before you apply for a Schengen Visa as a long term student, working permit or resident.
Remember, the documents to be requested may differ according to the purposes of the visit, the country and constant changes in law. There is a processing fee to apply and this varies according to visa, country and Consulate. Have your four copies correlated in the same order as the originals. Be extremely organized, present your paperwork to the agent in order and the process will be swift and hassle free.
Sit back and relax as the resolution of your application could take up to three months. The consulate will contact you via mail at an address in the United States only. You will have to return to the consulate once receiving the notice with your stamped copies of paperwork and passport to allow the consulate to affix the visa stamp. Once complete you are now free to travel to that country. Follow the instructions the agent gives you as to what procedure must be followed when you reach your destination for authorizing your new residence.