Personal Russian Visa is given to visitors who come to Russia to visit their friends, relatives etc. It can be valid for up to 3 months and is single entry only. You need to start the application process for this visa at least two months prior to the planned dates of a trip.
To obtain this visa, you need a personal invitation certificate (or visa entitlement certificate - "izveshchenie") from a person living in Russia. The person who invites you should go to their local OVIR (Office of Visas and Registration) office to fill in an application form. The OVIR officials will then give them a personal invitation certificate. This invitation can only be sent to you by post, because consulates accept originals only.