Kazakhstan is a big country with a population dispersed over more than 20 cities with over 100.000 inhabitants. If you have to move around quickly, you will be happy to find out there are many domestic flights. Almaty airport and Astana airport are now reasonably well-connected with Europe, Asia and the Middle East, with a minor role for Shymkent and Aqtau as international airports.
Next, you’ll need to manually check some of the smaller airlines that are not in the global distribution systems yet. If you are already in Kazakhstan, drop by your local “aviakassa” selling plane tickets. It’s what locals do. If you’re not, you’ll need to check the following by hand: Qazaq Air (new since 2015, I assume they will be included in GDS quite soon), Irtysh Air and Bek Air.
Inside Kazakhstan, 5 companies provide domestic flights: Air Astana, SCAT, Qazaq Air, Irtysh Air and Bek Air. They service those places you dread to take a train to, like Zhezkazgan or Aqtobe. If you need to get from Almaty to Astana or vice versa, there is also a quick overnight train you might consider. Be sure to book Astana – Almaty flights in advance, they sell out quickly. Especially weekends and holidays are popular moments to escape the capital.