I can only speak for Germany:
Teaching is done by professors. Sometimes they delegate certain courses to assistants (not TAs, usually PhD candidates or post-docs), but this is still counted as "teaching" by the professor (there are legal issues involved which I don't want to adress here, but this is the common practice). As a consequence, the assistant gains teaching experience (which is good and might help in further career steps!), but there is no additional financial compensation.
Usually, PhD candidates are hired for certain research projects or they are assigned to graduate schools, in both cases there is a salary / scholarship financing your work. In my discipline (computer science), this is less then a job in industry, but it's not bad (you might want to look up TVL-13 here). It depends on the culture of your discipline if you are getting a full salary or just 50% (in biology I heard there are people getting even only 25%).
In addition, universities might hire external visiting lecturers who are recieving up to 55€/hour, but at my university we were forced to lower the rate to 35€/hour (teaching hour = 45 min.). But usually those people have to be external, you can not be employed by the university and get this salary on top.
But in short: If you are getting a position in a funded project, funding your costs of living is not an issue.
BTW: Teaching can be done in German or English, depending on your University and course level.