Meat, potatoes, rice and pasta. And lots of it. If you're vegetarian be wary, because if it doesn't have meat in it, it was almost certainly cooked on meat stock.
Some recommended dishes:
Beshbarmak - a horse meat and pasta dish with potato and onion. The national traditional dish of Kazakhstan most often served for special occasions. Can also be made with beef or lamb. Most restaurants that serve it will present a portion enough for two or three people
Kazy - handmade horse meat sausage, could be cooked and served with Beshbarmak, but not at the restaurants, unless you ask to do so when preorder menu. If you did not, it would be served as cold meat appetizer with other types of cold meat appetizersZhaya, Basturma, Shyzhyk. And separate price would be charged. Kazakh dish.
Laghman - a thick noodle dish with meat, carrot and onion, usually served as a soup.Some other veggies could be added too.
Manty - large steamed dumplings full of meat and onions. Sometimes made with onions or pumpkin. Traditional Uighur dish.
Plov - wonderful dish of fried rice, meat, carrots, and sometimes other bits such as raisins or tomatoes. Traditional Uzbek dish.
Shashlyk or Shish Kebab - skewered, roasted chunks of marinated meat, served with some sort of flatbread usually lavash and onions. Various marinates can be used, and different ways to cook it, open fire or other.
Baursaky - bread best served piping hot. A little like an unsweetened doughnut. Kazakh.
Pelmeni - boiled dumplings made from different kinds of meat or potato. Russian.
If you're a vegetarian, you're probably thinking there's nothing for you in Kazakstan. And you're right - so long as you eat out. But if you're cooking your own food, you'll be more than satisfied. Kazakstan has some excellent products available at little markets everywhere. You will be amazed with the taste and availability of fresh organic veggies at low price! For a treat in Almaty, try Govinda's, a delicious vegetarian Hare Krishna restaurant. Malls have food courts with some vegetarian options too. Even some small Kazakh eateries will prepare vegetarian meals for you if you make it very clear to them e.g. "byez myasa" (without meat, "ya vegeterianetz" I [male] am a vegetarian, "ya vegetarianka" I [female] am a vegetarian in Russian). At some places e.g. smak you can even find vegetarian manty made with pumpkin.
The legacy of Korean resettlement in Kazakhstan means that Korean dishes, particularly salads, are very common. At the country's many bazaars independent food and goods markets, look for the Korean ladies selling these. They will wrap you up any number of delicious, often spicy and garlicky salads to take away in plastic bags. If you are vegetarian, this may be the only decent thing you get to eat while you're in the country.
On the other hand, in Kazakhstan you can find any dishes you want, but Chinese and Japanese dishes are very expensive.The most delicious is caviar, which is very cheap, you can buy 1 kilo of caviar for less than USD300 in Almaty Zyeloniy Bazaar, but you can't export or take it with you home, you will be stopped at airport and pay high fines.
Eating out is relatively cheap; you basically order the meat dish and then add rice, potatoes, etc. Each element is priced individually, so you can order for instance only meat or only rice. Prices are relatively cheap, count 500T for chicken, 1000T for beef, and up to 1500T for horse, a local delicacy. Of course, the fancier the restaurant, the higher the price. If you don't speak Russian, things are relatively hard as the majority of restaurants don't have English menus with the exception of some hyped places in Almaty.
While Kazakhs are not very religious, most do not eat pork. Be aware of this if you are dining out with Kazakhs or planning a dinner at home. Also many dishes that are made elsewhere with pork such as dumplings or sausage are made with beef or mutton here.