What to do if I overstayed my e-visa for Saint Petersburg/Leningrad Oblast

First of all, if you are not fluent in Russian, you'll need (this is mandatory) an official translator to a language you speak fluently (in my case it was English, even though I'm a German). The smartest way to get one is to call a translation agency - several of these can be found in the city. After that, this is what you'll have to do (the translator should be with you at all times, because the Russian bureaucracy is exclusively in Russian):

1. You need to go to the visa and passport office in Saint Petersburg and up to the third floor, the door on the right side.
2. In there your translator will need to fill in several forms, stating your reason why you've overstayed, as well as all you personal data in Cyrillic letters (including your address, work-address, position at work, private phone, work phone, place of birth, etc...)
3. In my case, it took a day until everything was finished. They informed my translator, and my translator informed me about the date and time for my court hearing.
4. At the court, it is highly recommended to plead guilty, because even if it may not have been your fault and there where no bad intentions on your side, you still are the one who did something wrong. Also you will be told your punishment, which is most likely a fee of 5000 rubles and, depending on the case and the mood of the judge, a five year ban from entering the Russian Federation. (This ban means you're being deported on your own terms and cost.) It's not recommended to fight this punishment right away; it's smarter to accept it and maybe fight the ban in a different attempt (if you have a reason to do so).
5. After that you need to pay the fee at the Sberbank and get 3 receipts: one is to be returned to the court, one is for the migration office and one is for you to show with the court order at the border (but you will be told about that again).
6. You now have 15 days to leave the country.
7. If you're deported (being banned), you can leave right away; if not, you have to apply for an "exit and transit visa"
8. You have to pay another fee of 1000 rubles for this visa at the same bank, but this time, one receipt will be enough. (Note: it seems like they've changed the name of that one, so the bank maybe won't know the fee by the name. I recommend to get the transaction number just to be safe.)
9. You need to apply for the visa in the same building, but this time the first floor, the door on the left, counters 5 or 6.
10. The documents you need to apply are: Passport, a copy of the passport, a copy of your plane tickets, a copy of every paid fine/fee, an id-photo, a filled-out application form, a copy of your migration card, a copy of your e-visa.
11. After 2-3 workdays (they don't work on Wednesdays), you can collect your visa and are free to leave the country.

Important: do not buy any tickets until you've got certain confirmation on when you'll be allowed to leave the country. My original ticket was for January 5, now my departure will be January 23.
Today (January 21) I got my visa to leave Russia. If you're in this situation, calculate at least 10 workdays for the process. Find a good place to stay and explore the city while you're waiting for responses.

If I forgot anything, please feel free to add it.