Buy an apartment in Moscow. Then you as the owner will be able to apply to the passport office and get permanent registration on the basis of documents confirming the right of ownership. If you have enough money, you can buy, for example, only a share in an apartment or a room in a communal. However, note that in the first case, you may be difficult to sell purchased housing.
Get a permanent registration in the apartment of one of the relatives or friends who already live in Moscow. To do this, it needs to be along with you to the passport office to present your passport and documents to the apartment and then fill out the form to confirm their consent to the registration in its housing. If he can't come in person, you can convey a statement, signed by his own hand, which will contain consent to registration you in his apartment. But the relative may arise reasonable doubts about whether or not he even register. In this case, you can say that if you have not lived in the apartment before privatization, registration gives you no rights to housing. You can be discharged by the owner, in rare cases - with the assistance of the court.
Please contact one of the organizations involved in the registration of residence for visitors. So you will be able to register on-site any houses where already registered a lot of people. Be careful. Some firms even go to the creation of false documents, for example, using a makeshift stamp of registration. Stay away from such firms-violators in order not to become liable for forgery.
If you failed to get a permanent registration, make the time. It will give you the legal right to live and work in Moscow. Such a residence permit you can obtain the owner of a rented apartment, you can also get if you live in a hotel. A temporary residence permit will allow you to keep a permanent registration in other city, if you have one.