By plane
There are airlines from Moscow-Ural Airlines and S7 Siberian have regular flights. Direct flights to/from Ekaterinburg are possible. For Moscow, everyone in Chita tends to take a train to Irkutsk and fly from there as to do so is much cheaper. There is also a twice a week hap-hazard service to Beijing via Hailer on Air China, but it is regularly cut short, requiring you to take the train.
The civilian airport Kadala is a few kilometres from the town centre, but rather than taking an expensive taxi to or from the city, hop onto a 'marshrutka' taxibus. In the city, these go from the large concourse between the train station and the cathedral- any marked 'аÑÑопоÑÑ' airport will go there.
The airport has very few facilities so bring food and drink if you plan to wait for a while you will probably have to wait 24 h or so anyway due to delayed flights, fuelling problems and drunken crew.
By train
Chita is served by the Trans-Siberian Railway.
By bus
A service operates to Ulan Ude, but the frequency depends on the season.