As an American, how can I gain employment in Europe?

I’m not married to anyone from the EU. I’m not wealthy or a celebrity. My Irish lineage is too far back to claim for passport purposes. I don’t have a PhD in medicine…but without these things I’ve not been able to find a way to live and work in Europe. It’s been a passion of mine since I attended college there for 5 years (almost 9 years ago) to return. I’ve had friends who have tried to employ me in their companies, but have had trouble proving that my skills as a graphic designer are more worthy than any EU citizen. And I haven’t found an American company with needs for a designer overseas.
Now that there’s Fluther I thought: Why not ask? Anyone with any ideas?