Much of the city center is walkable, and the main attractions for tourists (the Kremlin and Bauman Street) are only for pedestrian traffic. Public buses are abundant and cheap, but one must have some knowledge of Russian to read the signs or ask where the buses are headed.
For navigation use 2GIS, Yandex Transport or Google Maps.
Bus system maps are apparently hard to come by. Taxis are available and operate mostly an on-call service, rather than plying the streets for fares. One can also download taxi apps for your smartphone as Tap Taxi or Rutaxi. They also congregate at a few taxi stands in predictable places such as the train station. A Metro system is being developed, with ten stations on the red line in operation as of early 2013, running between Avivastroitelnaya and Prospekt Pobedy.
A free map is distributed at the reception of hotels.
A signle way ticket on metro/bus/tram is 20 rubles. There is a possibility to buy a travel card with the reduced fare.
You can rent a bike from one of several Veli'k stands placed in the centre of the city, but as it requires usage of credit card, the registering procedure might be confusing. Here are some of alternative places to rent a bicycle from:
This is originally a coworking space/cafe, so try to explain their friendly staff that you need one of the bikes to ride. After leaving some kind of ID (standard procedure for sports equipment rental in Russia), you'll be off with one of the cheapest bikes for rent in town (2 roubles/min for the first hour, then the price gets reduced to 1 rouble/min.) ☎ +7 843 253 5219
A recently opened spot has brand new bikes to offer for modest 150 roubles/hour (prices go down if you rent from 3 hrs up to 6 hrs, after that the freezepoint is 650 roubles which is a daily rental cost). Open daily 12:00-22:00