To start invoicing and collecting money in Germany, you’ll need to get a freelance Steuernummer or tax number (not the same thing as the tax ID you received after registering your address) — and that means filling out the Fragebogen zur steuerlichen Erfassung. It looks pretty intimidating at first glance, but for most freelancers a lot of the lines can stay blank.
Here’s a line-by-line translation to help you along, assuming you have a straightforward freelance occupation such as artist. (Note: some common jobs such as tour guide, cleaner, bicycle delivery person, etc. may not be classified as freelancing in Germany at all — but actually be a Gewerbe or trade, requiring you to get a Gewerbeschein or trade license.)