A private visa is required for visitors invited by their relatives or friends in Russia. Private (guest) visa is issued for a period no longer than 90 days and is valid for single and double entry. 
To apply for a private visa at the Consular Section of the Embassy you should have a prior appointment and submit the following documents in person:
1. Double sided completed application form http://visa.kdmid.ru, one per person. Application form must be signed and dated. Make sure your application is addressed to the EMBASSY OF THE RUSSIAN FEDERATION IN AUSTRALIA 
2. One professional passport sized photo (3,5 x 4.5 cm) The photo should be glued (not stapled or attached using adhesive tape) to the specially marked place of the application form.
3. National passport (original) valid for at least 6 months after the intended date of departure from Russia. At least one page of the passport should be free from notes.
4. Original letter of invitation issued by local migration office of the Ministry of Internal Affairs of the Russian Federation (can also be issued in an electronic form). Every invitation must contain name in full, date of birth, citizenship and passport number of the applicant, name of hosting organization, reason and period of visit. Invitation must be signed by authorized person and carry the official seal.
In case of urgent medical treatment in Russia or visiting seriously ill or deceased relative, instead of the invitation applicants can submit a certificate issued by a medical institution or a death certificate and a document proving the kindred between the applicant and the ill or deceased relative. 
5. Copy of itinerary (flight details).
IMPORTANT NOTICE
Applications for a Guest Visa concerning close family members of a Russian citizen (spouse, parents or adoptive parents, children, including adopted children, spouses of children, full and half brothers and sisters, grandparents, grandchildren) are accepted without the Invitation of the Ministry of Internal Affairs of the Russian Federation if they travel together and the Russian citizen has a permanent registered residency in Russia. In this case a multiple entry visa can be granted for the period of up to 1 year. 
Applications for this type of visa should be submitted to the Consular Section by a Russian citizen in person along with the following documents.
1.       Personal letter to the Ambassador (please indicate names, IDs, dates of travel, places to visit, your home address in Russia).
2.       Russian international and internal passport.
3.       Travel documents as proof of travelling together
4.       Proof of kinship (apostilled Birth / or Marriage Certificate etc.) 
Visa documents are accepted by the Consular Section from 9.30 am till 12.30 pm.
Single Entry Visa is valid for one visit to Russia within the specified dates of arrival and departure.
Double Entry Visa is issued for two entries (all arrival and departure dates must be indicated).
Multiple Entry Visa is issued for multiple entries. The validity period (from... until...) shown in a visa indicates only the length of time when multiple-entry visa holders may visit Russia. Please note that maximum duration of stay in Russia within this period can be no longer than 90 days. 
Please note that there is special timing for the visa issue in that exact case - this kind of visa can't be processed earlier that 10 days after the receipt of the application.
Please, carefully fill in the visa information in the application form and follow all other requirements when submitting your papers. When applying be advised that the permission to enter the Russian Federation is a courtesy of the State. 
Visa can be denied if the Consulate has serious reasons to believe that the applicant's visit to the Russian Federation is not desirable, and the disclosure of the reason for the denial can be withheld.
The validity and type of visa should be strictly connected to the purpose of visit. When in Russia, you cannot change your visa status i.e. from tourist to business or from business to guest and vice versa. To do that, you have to leave the country and re-enter on different visa.
After you receive your visa, please check it for possible mistakes (passport number, date of birth, term of validity etc.) and, if necessary, return it to us for corrections. The Consular Section will not be responsible for the mistakes, which were not brought to its attention before your departure from Australia.

ATTENTION! There are additional requirements for non-Australian citizens (permit to study, work in Australia for more than 90 days, resident permit, etc.).
Citizens of the Russian Federation, regardless of any other citizenship they have, must travel to Russia on valid Russian documents only.