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Hello Nadezhda,
In principle everybody needs to register and it is better to register anyway as the authorities at the airport very closely inspect foreign passports.
The process is simple: when you check into a hotel, they register you automatically. If he stays with you, you need to take care of the registration yourself. Any post office can do this for you.
I hope this helps. Sunny greetings, and have a great and joyful time in St. Pete!