One of the most important things to think about before going abroad is “can I handle it financially”. If your answer is “yes”, then you shouldn’t have any problems further. Just find an university and something you would like to study and just go for it.
If however you do need financial aid, one of the best solutions (known to me) is to apply for a DAAD scholarship (available in most countries worldwide). The process is pretty straightforward – application, interview and that’s it, you either get it or not. (More info: www.daad.de). After this step you need to get a position at the university and matriculate.
It is as easy as it sounds. Good luck!