The central part of Ekaterinburg has problems coping with traffic. Getting around the center of Yekaterinburg by car is a real pain. The public transport system, however, is efficient. There is a wide tram network that is inexpensive and reliable. Trams can be quite crowded and the ticket is purchased onboard. Buses and trolleybuses (electric buses) experience the disadvantage of heavy traffic during peak hours.
Yekaterinburg is a very compact city for its population (1.3 million). One can drive from one side of the city to the other in some 30 to 40 minutes, provided there is no traffic. Yekaterinburg has a single metro (underground train) line, connecting the central part (stop is near the Circus) to Uralmash — a large industrial and residential area, having stops near main railway station and further down to Uralmash. The metro (natives say it is the shortest metro in the world) has proved to be popular with locals because it is quick and inexpensive (2011: RUB18/ride). The stations are impressive, decorated with native Ural stones, granite and marble.
You can get free walking maps published by the "Ekaterinburg Tourist Information Service" at their office on 8 Marta St. 21, office 2 (620014 г. Екатеринбург, ул. 8 Марта, офис 2). Those include sightseeing and culture.
To get there take a metro train to ploshchad' 1905 goda (площадь 1905-ого года, square of 1905 year), walk away from the square, go straight across ploshchad' Malysheva (площадь Малышева) and it is the second house on the left hand side. They have merchandise in their windows (even GPS navigators) and you can enter from the court after you pass the house. There is an English speaker at hand and they can book tours as well.
If you can read cyrillic then you might get a good map from the railway stations and many street magazines called "Городской транспорт Екатеринбурга — карта с каждым домом" (city transport map of Yekaterinburg — map with all houses) which includes subway stations, all bus and elektrichka routes as well as three maps (inner city, big city, Koltsovo airport and surroundings) as well as a street register. By the same publisher, Urals Cartographic Company, Malysheva St. 122ze, 2F, Rm 207 (Уральская Картографическая Компания, ул. Малышева 122з, 2 этаж, к. 207), there is also a map called "достопримечательности Екатеринбурга" (Sights of Yekaterinburg) for about the same price of about RUB500.
If you get lost, there are information stands in the inner city around Square of 1905 that will show you your current location, a map of the inner city and possibly help you to find addresses, restaurants and sights. Though they are in Russian only, it should be enough to help you out.