Public transport in Astana
Bus 10 and Bus 12 connect the airport and the city center at least twice hourly, the price is 90 tenge. You can find the timetable at the bus stop directly in front of the main entrance to the T2 (domestic) terminal. It's a one-minute walk from T1 (international) terminal. A taxi from the airport to the city center is about US$ 5-8 (depending on the destination). For bus routes, times and real time location updates, download the very useful Astrabus smartphone app. Another useful app is 2GIS.
Taxi services are available in the city through Yandex, Uber, and Indriver applications. You can expect to pay 1000-3500 tenge for a trip within the city.
Astana 1 Railway Station (north side of the city). For timetables and tickets see https://tickets.kz/en/gd, https://railways.kz/. Three direct trains run daily between Almaty and Astana, taking 20 hours overnight. For Russia, there's a direct train to Moscow (not daily) via Petropavlovsk; or travel to Chelabynsk (18 hours) for connections across the Urals and European Russia. For Urumqi in western China, a weekly train runs via Karagandy, Aktogai, and Dostyk.
Astana Nurly Zhol railway station (10 km east of the city). Bus 50 runs frequently downtown, and Bus 48 connects the two stations. Check locally near the day of travel!
Saparzhay bus station (Автовокорский Сапаржай) (next to Astana-1 railway station). The city's bus station with arrivals from other major cities in Kazakhstan, relatively nearby major cities in Russia and Central Asia; as far as Tashkent and Yekaterinburg.
See the website for the full version with more information https://en.wikivoyage.org/wiki/Astana