There is a booming finance industry in Kazakhstan so international banking services are generally well-supported in all the major cities. You should be able to withdraw money with most bank cards (Visa, Maestro and Mastercard are commonly accepted), although expect it to occasionally get rejected. Most ATMs only dispense money in tenge but there are a few in the centres of the large cities that stock dollars. Ask the locals where these are located as they will probably know from their own use.
While travellers cheques are not accepted in Kazakhstan, it is possible to send and transfer money easily. Most banks are connected internationally and provide transfer services that don’t require much hassle. There is also a large number of Western Union branches, mostly concentrated in the cities, through which you can send and receive money easily.