Germany is “not a country of immigration”, as our politicians liked to say over the years. This is supposed to mean that, unlike the USA, Germany is neither based on immigration nor likely to see much, due to recent history. However, politicians were wrong and Germany is among the countries with the highest amount of (non-naturalized) immigrants worldwide. Anyway, because of that false belief, Germany’s laws are not well adapted to this situation, and Germany finds itself accepting a lot of unskilled workers (especially from Turkey or Eastern Europe) and asylum seekers, while doing a good job at keeping out highly-qualified professionals from first-world countries.

Your best bet is probably to come here as a tourist and then get employed with a German company (universities can employ foreigners with less hassle). If you have employment, and your employer is patient enough to wait for all the paperwork to go through, you may live and work in Germany for as long as your employment lasts. If you have worked here for at least 2 years without interruption, your next visa for staying and working here will be independent of your employment. This is done as a precaution against people coming here to take advantage of Germany’s great social net (universal healthcare, good unemployment money…). Chuck can tell you about this process in detail.

Unfortunately, due to the wrong belief I mentioned earlier, the most hassle-free way to get permission to stay and work here is to have German ancestors or to marry a German.