I am traveling to Seville, Spain with a friend for a study abroad program but the flight we found has a 23 hour layover in Dusseldorf, Germany. However, I am 16 and she is 17. According to my research, U.S. citizens do not need visas in Germany, but I am not sure about unaccompanied minors. Would we be able to leave the airport and what would we have to do in order to do so?
If you are flying from the US to Spain via Düsseldorf, you will clear immigration for the Schengen area on arrival in Düsseldorf. After that nobody is going to stop you from going wherever you like. For instance, you can take the SkyTrain directly from your arrival terminal to Bahnhof Düsseldorf Flughafen (Düsseldorf Airport train station; €2.60) and then get a train or bus to wherever.
Since you're under 18, you won't be able to rent a car. You'll have to use taxis, trains or buses to get around. You may also be unable to book a hotel room. If you haven't already made arrangements for your overnight stay in Düsseldorf, you should do so before you depart the US. Unless, of course, you actually want to sleep in the airport...
All this goes out the window if you are flying on a ticket with "unaccompanied minor" service. If you've booked this service on your tickets, you will be closely supervised and escorted throughout each airport by airline staff, will not be permitted to leave the airport at any layover, and must be picked up by an adult at your destination. And you will sleep in the airport.
On most airlines this is optional for travelers 15 or older, (12 or older for some airlines) and most teenagers will find it quite obnoxious, inconvenient, annoying, restrictive... If you've somehow ended up with this service, you may wish to change your booking to have it removed. If your parents stuck you with this, then it will almost certainly depend on convincing them that you aren't going to completely wreck the airport.