You need a work visa and a work permit to teach English legally in Russia. The work visa is the document you apply for at the Russian embassy/consulate in your home country, and this gives you the right to legally enter Russia for work. The work permit, a plastic card that you get when you arrive in Russia and pass the medical test, give you the right to work while in Russia.
Most language schools that hire expats are authorised to apply for work permits on the behalf of foreigners, and can grant them a letter of sponsorship that they can then use to apply for the appropriate work visa.
Most language schools that hire expats are authorised to apply for work permits on the behalf of foreigners, and can grant them a letter of sponsorship that they can then use to apply for the appropriate work visa.