Working in Germany without a German passport
The arrangements differ depending on your country of origin. Students from EU countries do not need work documents and can work just like German students. All other international students in Germany can work 120 full days / 240 half days per year without applying for a separate work permit. Please note, though, that this does not normally include self-employment or freelancing.
The most important exception from the 120 day rule is employment in a German university or public research institute where you are allowed to work more. Otherwise, if you need or wish to work more, you will have to require permission from the Agency for Employment. The Agency's approval is deemed to be given if it takes more than 14 days to make the decision. Even after completing your course, you are entitled to look for work in Germany with your qualification for a period not exceeding 18 months.
Know your rights
When working as a student, you are obviously not at the mercy of your employer's wishes. German employment law applies for you, even if you are "only" a student worker. You are entitled to regular breaks and sick pay if you are ill. If you only work particular days, you are still fully entitled to paid holidays on a pro rata basis.