Almaty International Airport is the largest international airport in Kazakhstan and is about 18km from the center of Almaty and typically takes between 30 mins and 50 mins to get there (depending on traffic).
Practically every part of the country can be reached by air from Almaty.
During the day you can take bus #92, #79. #106 and #86 to the city center, otherwise official taxis are available from the airport.