Usually foreign visitors to Russia from the West need a visa. To obtain a visa you need a valid invitation, which you need to submit to the Russian Embassy or Consulate together with an application form, proof of travel insurance, and a fee.
If you are travelling to Russia with a tourist agency, the agency will normally obtain your invitation for you and advise you on the application procedure, or undertake the application for you. If you are travelling privately, the person or organisation that is inviting you must send you an original copy (not a fax or email document) of a formal invitation that has been issued by the local police where you will be staying.. Needless to say, you have to allow adequate time for this process.
When you arrive in Russia you should to register with the local police according to the conditions stated on your visa.
THE CUSTOMS DECLARATION - ДЕКЛАРАЦИЯ
On arrival in Russia you usually have the option of going through a green or a red customs channel. If you go through the green channel with nothing to declare you do not need to fill in a customs declaration. If you go through the red channel you are able to fill in a declaration of money and valuables that you are carrying. Declarations are required if you are carrying large amounts of cash or valuable items. You should keep the declaration for the whole of your visit as you may need it on the way out.
When you leave Russia at the end of your visit you are allowed to export foreign currency up to the amount that you declared on the way in. In the event that you did not fill in a declaration on the way in, you may be asked where you aquired the money that you are taking out!. For this reason it may be a good idea to use the red channel even if you do not need to!