§ 55 of the German Industrial Code (GewO) explains which self-employed occupations are considered to be itinerant trades.
In order to practise an itinerant trade, you must apply for an itinerant trade card (Reisegewerbekarte) at your local regulatory agency (Ordnungsamt). This itinerant trade card is generally valid throughout Germany. However, the itinerant trade card can sometimes come with specific limitations, have an expiry date and have a number of terms and conditions. Whilst some jobs do not require an itinerant trade card, there are also jobs that you may not practise as itinerant trade occupations. You can find an overview here.