If you are going to Moscow you should get a visa in most cases. The list of countries of visa-free entry to Russia you can find here.
Visa to Russia can be ordinary, diplomatic, official, transit and visa for temporarily living person. The type depends on your purpose of the entry to Russia and the purpose of staying in the country. The ordinary one is divided into private, business, travel, training, work, humanitarian, and an entry visa to Russia in order to obtain asylum.
To spend several days in Moscow you need just ordinary tourist visa. It is issued for up to a month. Tourist visa is issued to person who has booked accommodation in Russia for non-business reason. It's best when you know exactly where and how long you will be staying in the country. For a tourist visa to Russia you should have an invitation. It's the confirmed accommodations or transit information for every night of your stay in the country. Here you can apply an invitation for Russian visa online and without any fees.
Ordinary private visa to Russia is issued for up to three months. Ordinary business one is issued for a term exceeding one year. In addition visa can be single, double and multiple. Validity of a visa may be extended during the stay of foreign citizens in Russia but it doesn't apply to tourist one.
For entry to Russia you should obtain and fill in a migration card. Also a tourist who has entered to Russia, is obliged to register within three working days from the date of arrival. To register you need to file a document confirming your identity and a migration card which has a mark of customs control.