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You can find information on Sofia city transport on their website http://www.sofiatraffic.bg/en/transport/121/marshrutna-mrezha. The subway is easy, you can just buy single tickets when you enter. To use busses/trams you can buy paper tickets usually sold on news stands. You can also buy a ticket from the driver though they may not have any for sale. If you have an android phone you can try Софбус 24. It's a useful app that shows when the next bus will arrive (they have GPS). I don't know if there is an iPhone equivalent.