Airlines
It is quite possible that your trip round Siberia will start from Novosibirsk. The city has the biggest airport in the region with a lot of international non-stop  flights. 
Airport “Tolmachevo” provides services for about 80 domestic and international flights. "Tolmachevo" is located about 20 km from Novosibirsk in suburb and headed on long distance flights. Regular flights connect Siberia with Europe (Frankfurt, Hanover) and Asia (Dubai, Tel-Aviv, Seul, Beigin, Urumchi, Tianjin, Tokio). There are up to  6 daily flights to/from Moscow and some to/from St.Petersbourgh.

Click links for current schedule (English):

Long-distant trains

Numerous long-distance trains run through Novosibirsk daily, including the Trans-Siberian, the Trans-Mongolian and the Trans-Manchurian trains. The trains go not only east and west, but also south along Turk-Sib line to Almaty, Bishkek and Tashkent. The main station of Novosibirsk is called Novosibirsk Glavny. The most comfortable way to get Novosibirsk from Moscow for 48 hours is using fast daily train “Sibiryak”. Eastbound there are usually 2-3 daily trains to Vladivostok (about 4,5 days), 6-7 trains to Irkutsk (31-35 hours) and 8-10 trains to Krasnoyarsk (13-14 hours). In the train timetable specified Moscow time (GMT +3 hrs).

Next link gives you complete timetables of domestic trains, buses and planes (in Russian only):