How to travel to Germany on a Budget?

It has always been my dream to travel to Germany and learn to read, write, and speak German. I am very intelligent and a very quick learner. The only way for me to learn the language is total immersion. I would like to try to stay for at least six months. I have looked at various language schools but they are way too expensive for my budget. How do I stay in Germany on a budget? $5000 - $10,000 is my budget . All money is in U.S. Dollars.

Your budget works out to EUR600-1200/month if you stay six months.
The minimum recommended budget for a foreign student in Germany is EUR700/month. It is possible to lead a simple life on that (incl. shared accommodation).
School fees go on top of this. And, if you don't have a full-time student visa, (compulsory) health insurance (minimum EUR150/month) also needs to be added.
Good luck!