If you’re from the EU, USA, Canada, Australia, Japan, or South Korea, you get an on-arrival visa in Kazakhstan for 30 days. Travellers from most Latin American countries too enjoy this privilege. Extending a visa can be tricky, but if you exit and re-enter on the same day, they renew your visa. However, they won't extend the visa for over 90 days.
When you enter the country, they give you an immigration form which you’ll need to fill in, and they stamp it twice. The second time is for police registration. Guard this form during your stay or risk a fine when it’s time to leave.