Your clinic should apply for a visa for you under the clinics name. This visa lasts for three months, but the clinic has the ability to extend these visas for three months at a time until you've reached the maximum of one year. In other words.. it's not a difficult process as long as the clinic usually takes international patients and has the license to apply for a visa. Once you're in Russia, it's a seamless process as you don't have to do anything yourself. As for applying for the visa before you arrive, they should send the visa invitation by mail and from there they will tell you what to do.
