Well, you just cannot move to Europe for a few years and live and work there.
Just like the United States has restrictions, so does Europe, and Switzerland
not being an EU country, it is even harder to gain entry for longer than 90 days (the length of a regular tourist visa) or even get a work permit.
Switzerland is notorious for being difficult and to gain entry to the work force
as a non-resident, it would take years to get finally a valid work permit.
Working for an international firm with satellite offices in Switzerland would
be your only way to gain entry and a job.
It's easier in EU countries but with unemployment quite high everywhere,
to get a work permit will be difficult as well. Freelance work on schools
teaching English would be doable, but you would need to contact schools
prior to moving there, as they apply for your work permit.
Each EU country has its own ruling towards work permits, and here you
can check the requirements of the country of your choice