The first step is always to approach a potential supervisor independently, present your own research interests and signal your interest in working with them, or to apply for an advertised doctoral position. Perhaps you already have good contacts that you can use or, conversely, you have been offered the supervision of your doctorate? You can find detailed information on the supervision of a doctoral thesis here.
In addition to clarifying who your supervisor(s) will be, there is another procedural step: The Faculty's Doctoral Committee must officially accept you as a doctoral candidate. The documents you need to submit for the application for acceptance as a doctoral candidate can be found in § 6 RPO [OP2] and the doctoral regulations relevant to you. Then enrol at the student office at the university.
What happens afterwards depends largely on the faculty in which you do your doctorate, how you finance it and what individual agreements you make with your supervisor(s). Will you take up a position as an academic employee, take on a part-time job or be able to use all of your time for your doctorate because you have a scholarship or your own reserves? Do you already have an existing network or do you still need to build up good contacts? Are you planning to take part in a doctoral programme?