Getting a work permit in Russia is not usually an easy process, at least if you are not a former Soviet Union state citizen. Sochi can possibly be an exception, as in nearest future the preparation of Olympic Games will create many new workplaces. Some of the potential vacancies will require international expertise. Highly qualified international candidates will have simplified visa and work permit procedure.
Another Olympics-related opportunity is to join Sochi 2014 Volunteer Program (recruitment will start on February 2012).
Apart from Olympics there are potential vacancies for English tutors, as the demand for English study in the city is constantly growing. It is also possible to find sport instructors' jobs, in both winter (skiing, snowboarding) and summer (diving, yachting, kitesurfing) sports, but the knowledge of Russian is essential for those positions.