Registration

If you have a tourist visa, then you will have to register your hotel. If the visa is private, the locals who invited you. I'm not doing its guests private invitations, it is not profitable. I buy a travel company invitation and register their guests at them. It is easier and faster. All under the law...

Thanks RealRussian for your comment! Indeed I got an invitation letter which stated that I'm going to stay in hotel in St. Petersburg but I'm not going there. I will stay in Moscow and around Golden Ring.

That's right! Just do not forget to register in the hotel. In Moscow decided where to stay and what will you watch?

Just do not forget to register in the hotel.

Why should the OP have to register in the hotel? These invitations are mostly fake (for travellers who don't know where they will stay), and no one ever goes to the hotel mentioned on the invitation as far as i know.

This is not a fake! This is a legitimate invitation on behalf of the travel company. A residence registration in Russia is easier to make them the same. You can live where and from whom you want, it's your right.

So I have to stay at least one night in a hotel or hostel which will make a registration for me or should I ask my hosts (couchsurfers) to do it?
They have to write anything in my passport or what that I avoid any problems at the custom?
I traveled so far 120 countries and Russian immigration egulations seams one of the most complicated...

No, it isn't obligatory for you to spend the night there. When crossing border, you fill in the migration card which part remains at you. On it give a mark. Everything simply and quickly.

@RealRussian: I mean it is ´fake´ in the sense that it is a legitimate invitation with which you can get your visa, but with a fake reservation on it (a place where you never have to stay).

Indeed the Russian rules can be pretty complicated Nikel :)

Exactly. You didn't like hotel, after all on the picture it was another and you have the right to leave from there. Such situation can be in each country, isn't it?
It is difficult to foreign citizen to understand the Russian rules sometimes. The Russian law sometimes can be "turned" in any party. And everything will be under the law! About it even there is a popular Russian saying ))