Anyone who is self-employed but not a Freiberufler runs a Gewerbe. You register at the Gewerbeamt of your city, which then informs the tax office.
Trade income can be subject to trade tax, although there is an allowance and a credit against income tax for sole traders.
Full guideHow to register as a freelancer in GermanyRelated terms
General information on German tax law, not advice on your individual case.