Flights to Almaty most commonly transit through Istanbul (Turkey), Vienna (Austria), Frankfurt (Germany) and Moscow (Russia). The main Asia links are Ürümqi (Xinjiang, China), Islamabad (Pakistan) and New Delhi (India). Some smaller Kazakh cities have international flights but rarely to anywhere except Russia. Long-distance rail connections include a daily Moscow-Almaty service and another line to Almaty from China via Ürümqi. The latter route is notable for the unpleasant China-Kazakhstan border crossing (think eight hours, no toilets, plundering officials). There's an overland route from Ürümqi to Almaty via the border post at Khorgos and Zharkent, accessible year-round. There are two other China-Kazakhstan crossings farther north, at Bakhty (Tacheng on the China side) and Maikapchagai (Jeminay in China), but it's a toss up whether they're open to foreigners. There is also a once-weekly ferry from Baku to Aktau in Kazakhstan, although there is no set schedule for depature. Just turn up at the port and ask about the next available departure. A ticket is USD 50.00 and the trip takes 18 hours.
Flying saves time and takes the tedium out of Kazakhstan's long distances, but it is the least edifying and arguably the least safe mode of transport in the region. However, for some destinations, and in some seasons, flying is the only sensible option. Helicopters are often available to get to hiking and skiing destinations that are way off the beaten track.
Trains are cheap, slow and easy going, but crowded, grotty and increasingly crime-ridden. Buses are the most frequent and convenient way to get between towns cheaply, and the best way to see what remains of the land of the nomads, though long trips can be tedious and cramped, and vehicles are prone to breakdowns. An option in many areas is to hire a car and driver: taxis and private citizens are often willing to take travellers between cities.