A lot of people have the same problem. The Schengen visa lets you travel through most of Europe for 90 days within a period of 180 days (6 months). This visa does not give you the right to work though.
In many places acquiring a work permit for a hostel position is nearly impossible, even if the hostel wants to hire you. The hostel has to give EU citizens the first shot at the job, and then if no one is qualified, then they can open it to candidates from outside the EU. The catch is that you (and the hostel) will have to demonstrate that you are more qualified than anyone else in the EU for that position. Don't let me discourage you though. Apply anyway, because it's always worth a shot!
Some other options that might allow you to stay in Europe legally:
- Register as a full-time student at a European university. This may give you the right to work part time.
- Participate in one of the English Language Assistantship programs that exist in a number of countries. The programs are government run and involve a long-term visa. Technically you can’t work another job simultaneously with that visa, but many people do anyway. (I was actually told by the embassy representative that I should look for under-the-table work to supplement my salary when I did this in France)
- Get a job with a US-based company, and ask them to transfer you to a European branch.
- Look for Internship opportunities abroad. For example, AIESEC is an organization that frequently facilitates international internships. I believe they also assist with visa issues.
- Start your own business in a European country. Some countries make this very difficult for a foreigner to do, while others are more relaxed.
- Invest in or become a partner of an existing European company, such as a hostel.
- Marry a European citizen and gain full working rights.
- Adopt a European child. Amazingly enough, an Immigration officer once gave me this sage advice. He said that I didn’t have 9 months on my visa, so making my own wasn’t an option. I could, however, try to adopt one during my normal 90 day visa. I was shocked, but I’ll pass on his words of advice anyway.
Maybe someone else will have some other ideas for you based on their own experience.
Best of luck hopping continents!