if you are on a very small budget, but not on a tight schedule, you may try to place a request, or check for offers, at a website for private car-pooling like http://www.mitfahrgelegenheit.de/#
At the same website you can check for sharing a train ticket, too. Berlin-Chemnitz is roundabout 10 €. Filling up the number of participating people up to max allowance of a group ticket, is pretty common, and absolutely legal in Germany.
Also the good old hitchhiking less common nowadays, but still possible. Check this:
Enjoy your trip.
KKEdited: 09 June 2011, 18:29