Usually there is a section on TA about 'Arriving and Departing' under Travel guide for all the cities. But I couldnt find that for Novosibirsk. Having spent the past few days in Novosibirsk, I thought I will post some information regarding that here.
Novosibirsk is serviced by Tolmachevo airport.
To get to the city centre, obviously taxi is the simplest and most expensive method. The cost is about 300-350 Rubles, depends both on how good you are and how bad the cab driver is. For example, the driver who approached me, asked 300 Rubles to the city centre. Either he was really honest, or I was lucky, or I didnt understand what he actually meant.
The best method however is to take the shuttle bus to the main train station (Novosibirsk-Glavnny). Its good to remember the station name (and Airport for that matter) in Cyrllic alphabets. Because the signs are not in English. The buses wait right outside the airport when you come out and are grey in colour (usually). Apparently they run twice/hour. The trip takes about 35-40 minutes (add more time when high traffic) and cost you 30 Rubles. The bus should drop you in the main square in front of the train station. From there you could easily spot the 'M' sign for Metro (Green/Blue line). You can take the bus back to the airport from the same place. Interesting but not important information: You board the bus from the second door (not through the door in front of the driver) and you pay at the end of your trip.
Once you find the metro sign, go down and take the metro. Since this is the end (or beginning) of the line, there is only one direction you can go. A single trip in metro costs you 15 Rubles. You will be given a coin rather than a ticket. Transfer into metro to go to Kransky Prospect which is a major station and also where Red line connects. You can change to Red line to go to Lenin Place/square which is another major station. This is where the State Theatre of Ballet and Opera is located.
Hope this information is useful.
For 2c worth, I took a totally different route to City which involved a mini bus and a bus. In the mini bus, the lady charged me 50 Rubles, even though there was a big sign right in front of me said the charge is 14 Rubles. And she got 14 Rubles from everyone else sitting next to me as well. She probably thought I couldnt read but then, I was under her mercy to show me how to go to where I wanted to go. So I paid without any complaint.