If you have permanent EU residency in Italy (this is called ‘soggiornante di lungo period – CE o UE’), you can enter Germany and apply for a residence permit here.
If you have any other type of permit, you have to first get a visa from the German embassy in Italy.
It is not clear to me what you mean by coming to work as a working student to Germany. To work part-time as a student in Germany, you need to be studying here. Do you intend to continue your studies or do an exchange semester in Germany? Then you need to apply for a student visa from the embassy.
Here's the information from the website (in Italian) about the requirements for a study visa: