You do not have to pay for education in a public school. However, the pupils may have to pay expenses for excursions and learning materials. If You choose a private school, you have to pay the fees of this school.
Under certain circumstances, funding is possible under the Federal Training Assistance Act (BAföG) or the so-called "Ascension BAföG".
There are no fees for attending a public school. If you choose a private school, you have to pay the appropriate school fees.