Most of the people who come to Germany from abroad learn German as part of an Integrationskurs (integration course). Here (Information sheet 'integration course') you can find out about the syllabus taught in an integration course, who is entitled – or even obliged – to attend such a course, how they are organised, and where details of the courses on offer can be found.
Search here or here for current courses
The learning portal of the German Adult Education Association enables migrants who do not currently have a place on an integration or German course to learn the language free of charge and to a high standard. Link to portal