The answer is so simple it's brilliant: you need a permission from the local police in order to organize a protest on a specific location at a specific time. In most of the cases, that works fine.

In a small number of cases when the authorities really don't want you to organize a protest, they'll keep denying you one location after the other using bullshit excuses until the date when the protest is set to happen. Then they can crack it down for "unlawful assembly".

Note that I'm not from Russia, but I am from a country that looks up to Russia for some forsaken reason and we have experienced protests getting killed in this fashion.