As of August 2012 international students who do not come from the EU or EEA are allowed to work 120 full or 240 half days in a year. To do this they do not need authorisation from the Employment Agency, i.e. the German authorities.
International students who do not come from the EU cannot go self employed or work freelance!
If you want to work more than 120 full or 240 half days you need the approval of the Employment Agency and the Aliens Department. Whether you receive the approval depends on the situation of the job market in your place of study. In regions with high unemployment you will have little chance of working more than 120 days.
One exception, however, is the occupation of academic or student assistant. As long as your studies are not impaired by it, this work can be carried out for an unlimited period of time. The Aliens Department must still be informed if you wish to work as an academic or student assistant!
If you attend a language course or study at a preparatory college the regulations are stricter than for normal enrolled students. You are only allowed to work with the approval of the Aliens Department and the Employment Agency - and only during lecture-free time.
Basically students from the European Union and the EEA stand practically on equal terms with German students and have free access to the German job market.
Since Mai 2011 students from Estonia, Latvia, Lithuania, Poland, Slovakia, Slovenia, Czech Republic and Hungary can work in terms similar to the German students.
For students from Bulgaria and Romania the restrictions of 120/240 days still apply. If you come from one of these countries you only have limited access to the job market and you need authorisation from the Federal Employment Agency. This authority checks whether or not a German citizen or any other EU-citizen is available to do the job.
If you do not come from the EU or the EEA and have a work placement in Germany it counts as normal work - even if the placement is unpaid! Every day of your work experience will be subtracted from your 120 days.
For example, if you have already worked 120 days you must get authorisation from the Aliens Department and the Federal Employment Agency to be able to do a work placement.
The only exceptions are work placements that are a compulsory part of your studies.