You can start with school training in Germany at any time. Vocational training or higher education is already possible four months after submission of your application for asylum. With a residence permit or tolerated status where a work permit has not been refused, you can go ahead straight away. For further information, see Access to the labour market.
Vocational training in Germany is generally conducted in a dual system, which means that the in-company practical phases alternate with school training. So you must apply for training places at businesses, but you will receive assistance for this from employment agencies or job centres. You can obtain further information at Getting help.
The requirement for a course of study in Germany is a certificate in keeping with the legal provisions of the country where it was obtained that qualifies you for university entrance. This is based on assessment proposals of the anabin database. You can find a suitable higher education institution in Germany with the Higher Education Compass.