The easiest way to obtain a Green Card is through the Green Card Lottery. The U.S. government allocates 55,000 Green Cards every year as part of the Diversity Visa Program. Although, of course, a good deal of luck is required, nevertheless for many people this option is still the only way to realize their dreams of living in the United States. Several thousand Green Cards have been awarded in this way alone to participants from German speaking countries.
The American Dream also offers extensive services specifically aimed at the lottery.