Doing visa stuff isn’t fun. And the Berlin bureaucratic system is currently overwhelmed, so it is even more un-fun.
But anyways, there are two main ways that I know how to get an appointment:
- write your responsible department via the contact form or email.
- use the online booking system (otv.verwalt-berlin.de)
If you use the online booking system, you will often get an error:
⚠️ There are currently no dates available for the selected service! Please try again later.
⚠️ Für die gewählte Dienstleistung sind aktuell keine Termine frei! Bitte versuchen Sie es zu einem späteren Zeitpunkt erneut. 
This is normal, it means that there are no free appointments for you at the moment. If you want to get one, you just need to keep trying and refreshing the page by clicking the “next” button.
But clicking the button over and over is very annoying, so I have made a program to do it automatically for you.
If it gets to the calendar page, it will play an alarm. When the session expires it will play a different alarm, so you know to complete the form and start the program again.
Not convinced yet? Read the reviews –> https://chrome.google.com/webstore/detail/berlin-appointment-helper/ngdeikpgeefjhldilcfpjnppmpaagnae/reviews