What do I do when my employer is not giving me the minimum wage, not giving me the holiday I should get, etc.? What do I do then?
It’s all in the labour law. You should go to your employer. And it’s not just about those things, it’s also when the constitutional rights there applies you have freedom to express your opinion, you have the right for equal treatment, no matter where you are from, what your race is, what your gender is, if you are man or a woman, what your religion is. So these are all your rights, you have as an employee. If you find your employer does not follow those rights you have the right to complain and go to them. Also when other colleagues don’t treat you right, you have the right to complain. If your employer doesn’t react you could even go to court. Or go to the Arbeitsagentur and say I’m not treated right and they can tell you what needs to be done.
Most big companies in Germany they have a work councill, a Betriebsrat, this is a organization that takes care of the employee’s rights. So if you feel that your employer doesn’t treat you well you can always go to that person in the company and they will help to defend your rights.
The employer pays half of your health insurance but they also have to make sure that your health is protected while you are working, so you don’t injure yourself, you don’t have accidents during your work, you don’t do anything that’s unhealthy in your work. For example That you have a good chair to sit on so you don’t get back problems.
like Isabel said you should ask your local work council or a member of a labour union for help.
Besides it's good to get your own informations about your rights. Some sources of information (English):
Minimum Wages in Germany: tinyurl.com/mt35zj8
Services of the Federal Ministry of Labour and Social Affairs: tinyurl.com/yat5gal4
German Confederation of Trade Unions (DGB): en.dgb.de/
German labour law and work contracts (by Expatica): tinyurl.com/ya7z9fqa