"I do not speak German at all."
Translation:Я совсем не говорю по-немецки.
My native language is Serbian, but I'll try to explain. Немецкий - it is an adjective. Немецкий язык - German language. Немецкая компания - German company etc.
But, when we write по-немецки, по-английски, по-русски etc. it means to do something in German (English/ Russian) style. But, how did the last й disappear? It is because we remove the whole ending ский and then add a new ending ски. Also, you can say по-свойски (in your own style). We had свой (own) and then add the ending ски.