To obtain Kazakh visa you should have visa support or letter of invitation from Travel Agency or any person. But the citizens of the following countries, wishing to visit Kazakhstan for the purpose of tourism, diplomatic, business or private visit, will not need visa support and invitation letter, if they apply for single visa only:

Australian Union,
Austria,
Kingdom of Belgium,
United Kingdom of Great Britain and Northern Ireland,
Greek Republic,
Kingdom of Denmark,
Irish Republic,
Republic of Iceland,
Kingdom of Spain,
Italy,
Canada,
Liechtenstein,
Luxembourg,
Malaysia,
Monaco,
Kingdom of Netherlands,
New Zealand,
Kingdom of Norway,
Portugal, Singapore,
United States of America,
Finland,
France,
Federal Republic of Germany,
Swiss Confederation,
Kingdom of Sweden,
Japan.

In this case you have to apply to Kazakh Embassy and obtain your visa there. But if you would like to have multiply visa, you should have letter of invitation. Probably the best way to do it is to use service of local agency which has a necessary authority to invite foreign citizens.
The visa process will take up to 3 days. After you have to receive your visa invirtation by fax or e-mail and visit Kazakh consulate with this invitation letter and got the visa there.

1. The visa application form , obtained from the Consulate, travel agencies or visa services must be filled out in print letters or typed. To issue such letter, travel agency should be provided with the following information:

# full name of the passport holder
# date of birth
# date of passport issue and expiration
# place of issue
# nationality (citizenship)
# travel dates

2. One passport size photo of the applicant.
3. Applicant's passport (not a photocopy).

Permits
# OVIR Registration. It is required to register with the Office of Visa and Registration Department (OVIR), within 3 business days after arrival in Kazakhstan.
# Special Permits: There are some regions in Kazakhstan that one can't access without a special permit. So, one planning the trip to Inylchek has to obtain special border permit. Border permit it is permission to visit border zone close to China, as you know China\Kazakh board is going over Khan Tengri, Marble Wall, so it needs special permit for anybody to visit this area, as from Kazakh side, so from Kyrgyz. Royalty it is climbing\trekking permit for climbing in this areas, only Kyrgyz side of trekking and climbing you have pay for that. Kazakh side for visiting or trekking and climbing is free.

To learn more you can also visit such a useful link:
http://www.traveldocs.com/kz/er.htm visa application form and regulations for the USA citizens
http://www.kazakhstaninvestment.com/kazakhstan-visa.html visa procedure and regulations