Many registration offices have introduced an appointment requirement during the corona pandemic, and most of them still have this requirement and are unlikely to disappear any time soon.
You should therefore not drop by the authority on the spur of the moment, but find out in advance on the Internet whether you need an appointment. Most registration offices allow you to book an appointment directly online.
You must submit the following documents when registering:
Here again to print out: Checklist: Documents for admission
Ideally, you should already reserve your desired license plate online.
Beware of offers on the Internet, there are a lot of "official" looking websites that offer to reserve your license plate for a fee. However, you can also reserve license plates on the website of your registration office - completely free of charge.
After your reservation you will receive a confirmation or a PIN, which you take with you to the registration and have your desired license plate number entered.
The costs of a license can vary from authority to authority and are not regulated nationwide, but you can use these values as a guide: