Finding a job is, to a certain extent, not as hard as dealing with the morass of paperwork that must be filled in prior to arriving. Getting an invitation to visit Russia, as well as a visa and a work permit takes a considerable amount of time and money. In fact, such is the difficulty of acquiring a temporary residence visa that many aspiring workers choose instead to apply and then re-apply for a business visa (each one lasting for one year). To make things even harder, if you wish to stay in Russia for longer than three months, you will have to have a series of medical tests, including those for HIV, TB and VD.
The most common profession for foreigners is teaching English, and there are a whole host of schools in the major cities that can be contacted about jobs, most of which offer accommodation as part of the contract. That said, there are other possible avenues if you are prepared to search. A good place to start is the list of websites on Anywork Anywhere.