The procedure of obtaining a Russian residence permit (green card) is generally the same for all nationals: Americans, Canadians, Indians, or South Africans.
An applicant is required to confirm at least basic knowledge of Russian language, history and law, get necessary medical certificates and prepare a package of documents. The exact list of the required documents may differ depending on the specific situation. Some categories of applicants are eligible to apply for a residence permit under simplified procedure which implies shorter processing time period as well as some other privileges.
When everything is ready, an applicant has to submit all the documents to a local office of migration authorities. The processing time may take for up to six months.