Buses & the Trolley Bus in Russia are Private and Government operated. The private ones cost more but are in better condition. The government ones are in very poor condition. No seating restrictions either, so be prepared to become a sardine. Don't be shy when lining up to get on the bus, push your way on as soon as the bus pulls up, or you will be left behind or pushed out of the way. Russians are very aggressive getting on buses, this will take some getting used to.
Also it is still customary to give up your seat for elderly and women with children. As for paying for the bus fair, some buses you pay the driver as you get off the bus, other buses a person will come around on the bus and collect the fair from you and give you a ticket. Or you must put the ticket in a hole punch attached to the wall of the bus, and punch your ticket, if there is cardboard stuck in the hole punch, this means there is someone on the bus who will come to you and check to see if you have a ticket or sell one to you. Other buses you just buy a ticket from the driver and then punch the ticket. There are fines for not buying a ticket (about $2 US). Ticket prices vary depending on where and what kind of bus you use, anywhere from a 10 cents to $1 US dollar approximately.
Bus fair prices are usually posted above the driver, or on the window near the entry, exit doors. On longer bus rides to other villages bus prices will be more, but the bus is very inexpensive to use in Russia, but of course all services are provided in Russian only. Also don't be surprised if your bus breaks down, or just doesn't show up as scheduled. This is a common occurrence, and they will just abandon you, don't expect them to make arrangements for another bus. In Moscow you can buy a bus ticket that’s good for three months and can be bought at a booth near the bus stops, they are good for one use. They are a different color every three months.
The Trolley Bus is very cheap only .5 cents USD to use, but is also in very poor condition in many places.