Astana is the capital of Kazakhstan.
From the southeast corner of ul. Respubliki and ul. Kensary take bus 9 or 111 to the stop Vstrecha. The ticket collector on the bus can tell you when to get off. From here, take bus 129 to the very last stop. This will be several kilometers out of the city on the beginnings of the road M36. Near the bus stop is a small police checkpoint for trucks, but walk further down the road until the main police roadblock for the area. Here cars slow down to 30 km/h and are easier to stop. If going further south than Karaganda, a sign is recommended.
From Astana, take the bus #24 and start HHing on Ondiris Road. Be aware that if you are not a Russian or Kazakh citizen, you won't be let through the border near Kishkenekol! You need to go through Petropavl.