If you have only just arrived in the country, you won’t be entitled to follow an integration course immediately. You will be issued a certificate of eligibility (“Berechtigungsschein”) once you have officially applied for asylum and fit the appropriate residence criteria. The website of the Immigration Office has a lot of useful information about this. While waiting for your certificate of eligibility, you have a number of other options. In many cities, you will find free German classes run by volunteers. A lot of these courses take place in initial reception centres, refugee homes or social and cultural venues.
If you are unsure which NGO or association to contact, you can ask local charities like the German Red Cross (DRK), AWO, Caritas or Diakonie for help. On the website of the BAMF you can also find your local advisory center (“Migrationsberatungsstelle für erwachsene Zuwanderer” or “MBE”). In addition to these free classes, you can find a variety of German courses online, including websites, video tutorials and apps. A number of them were developed by German cultural and media institutions, e.g. the Goethe Institut or Deutsche Welle.