I recently got an email from a young Anglo-Saxon reader of this blog. He's got a couple of college degrees under his belt. He'd met some Germans and rather fancied coming to the country to continue his studies or get a job. Here is the advice I'm giving him. Feel free to add your own in comments.
Your best chances might be academic; since there’s a pretty good infrastructure for arranging for students to visit and study in Germany. The chance would present itself to write a dissertation at a German university. Many of them will let you do this in English – although the life of a graduate student in Germany is no less precarious than it is in the States. There's a lot of red tape, and accommodations are basic, although acceptable.
Keep in mind that if you stay long-term, you will have to learn German at a pretty sophisticated level, not only for bureaucratic reasons but also for peace of mind. Like most Europeans (and people in general), Germans instantly judge foreigners by the care with which people speak their language, and you will soon get tired of being condescended to because you are speaking what sounds like 'pidgin' German. At some point, you will have to actually learn the three noun genders (distributed randomly) and the four cases if you want to communicate effectively and be treated with respect in a work or academic setting. You can't 'pick up' proper German. The non-Germans who say this are usually speaking crappy German themselves, although you may not realize this until it's too late and they've taught you a lot of errors. So, learning German will unavoidably require good, solid German classes (which are easy to find and available at all price levels). But this is a feature, not a bug! Language classes are a blast -- you get to regress to childhood, social distinctions are erased for a brief shining moment, you learn lots of interesting stuff about other cultures, and you can meet lots of intriguing members of the opposite sex (if that's your thing).
As for living and working, I can tell you one thing up-front: it is much, much easier to get settled in and have a pleasant and productive time if you are invited by an institution (whether for employment or for study). The more resources the institution puts at your disposal in terms of clearing paperwork hurdles, the better. Coming to a German city ‘cold,’ with no job and no connections, is a terrible idea. You will be soon be entwined in yards of red tape, the authorities will not be friendly toward you, and unless you can get a job within a few months, you will be forced either to work “black” (underground) or be put on a path to being chucked out of the country.
And getting a job without connections or valuable job skills is extremely difficult. As a practical matter, the only thing that offers itself is teaching English. While this can be a pleasant enough occupation on its own, it is fraught with difficulties. The pay is low, the work is sporadic, the competition is intense, and believe you me, a substantial minority of people in this profession have decided to go to a foreign country and teach English there for less-than-wholesome reasons -- if you catch my drift. So, I’d strongly suggest coming as a student, if at all possible. If that doesn’t fly, I would try to work contacts among the students you know to try to find some sort of work. Perhaps you could join a few of them for trips to Germany, and try to schedule a meeting or two to probe job opportunities. As always, the more specialized skills you have, the better your chances of getting a job that will offer you a dignified existence.
If you can work something out like this, though, I would say by all means come. It’s a beautiful, fascinating country, and the quality of life you can enjoy even on a limited income is impressive. Germans are thrilled by foreigners who have a genuine interest in their country, and will treat you to all sorts of unforgettable experiences.