We've got four cellular companies and all four offer prepaid sim cards.
Here are the links to their websites, they have english versions and maps of their sales offices. http://kcell.kz, http://beeline.kz, www.tele2.kz, www.altel.kz.
There are a lot of small reseller offices in the airports, train stations and shops, but they generally don't speak english (except maybe in the airports).
Bear in mind, that the only provider of 4G is Altel, so if you definitely need 4G that's your only choice. The speed of 4G is questionable, though.
All other providers offer 3G only.
Kcell and Beeline traditionally offer best coverage and quality of service, but the other two offer discounted rates. So, choose for yourself.
Yes, you are required to present your ID by legislation.