A short time ago I started with my PhD in mathematics (in Germany, too). IMHO it's rather difficult to get a "Doktorandenstelle" (salary for doing PhD). The reason is that many universities are (in my opinion) underfunded. If you get one - lucky you.

The only other possibility for getting money for doing your PhD is trying to get a scholarship. If you aren't near to either a big religion or a political party (I'm not to any of both), there's virtually only "Studienstiftung des deutschen Volkes" (German National Academic Foundation) which has really strict (and many people say: really strange) conditions of admission.