A repost of an answer to a similar question:

PART I

When the Russian (then technically Muscovite) state began to expand Eastwards into Siberia in the late 16th and 17th centuries, it largely bypassed the steppe zone. The expansion was in large part driven by the fur trade (from such animals as beaver and sable), and by this standard the steppe areas were not especially prized. The Russian state was mostly concerned with holding a frontier, and to this end a series of forts were established (Uralsk in 1584, but most of the others - Orenburg, Omsk, Semipalatinsk, Petropavlovsk in the early 18th century), and the frontier was largely policed by Cossacks (sidenote, the Russian word for Cossack is "Kazak", while "Kazakh" is the separate ethnic group that Kazakhstan is named after. Confusingly, until the Soviet era Kazakhs were called Kirgiz).

Now the regions south (-ish; it wasn't a very hard border) of the Russian frontier were inhabited by Kazakhs, who were pastoralists (they get called nomads, but this can obscure more than it enlightens, given that most of them engaged in some limited agriculture and traveled seasonally between designated pastures). The Kazakhs had united as a Khanate under Janibek in the late 15th century, but by the 17th century were much more loosely connected to each other, and were divided into three Hordes (Greater/Older, Middle and Little/Younger). The Hordes themselves were very loosely organized, with Khans largely chosen by tribal and village (aul) elders. And having divided pastoral groups on its southern frontier that mostly engaged in conflict with each other, with the sedentary states to the South, and with other nomads like the Dzhungars to the East suited Russia just fine. Kazakhs weren't even as deeply involved in internal Russian conflicts as, say, the Bashkirs and other Ural peoples were in Pugachev's revolt (although there was some Kazakh participation).

During this period, cooptation of Kazakh elites and pacification of the region to promote trade (not specifically trade with Kazakhs - the caravans were crossing the steppe between Russia and the settled parts of Transoxiana south of the steppe) was the favored means of Russian control over the Kazakhs, rather than annexation. Abul Khayr Khan of the Little Horde requested citizenship and protection from Empress Anna in 1730, and this began the Little Horde's status of effectively a Russian protectorate. Ablai Khan of the Middle Horde followed suit, swore loyalty to Russia in 1741 and was formally given the title of Khan by Catherine the Great in 1777.

Part of what motivated these Kazakh khans to seek recognition and protection from the Russian state was not only because of their interminable conflicts with other competitors for the title of khan within their Hordes, but also because of the wars that these Kazakh Hordes were fighting with the rapidly-expanding Dzhungar Khanate (based in what is now northern-Xinjiang). These conflicts intensified during the mid-18th century, and the Kazakh Hordes more often than not were on the losing end, and were eager for refuge and pasture area. When the situation was reversed in the 1750s, with the military defeat of the Dzhungars and arguably their genocide at the hands of the Qianlong Emperor, the immediate pressure on the Kazakhs was relieved, but they also faced a powerful new imperial neighbor who had inflicted a destruction on the Dzhungars far worse than the protectorate status offered by Russia. I should note that I'm simplifying the politics in this period considerably - Ablai Khan did swear fealty to the Qing Empire for a while, so Kazakh leaders were willing to play any side to their best advantage.

As for acculturation: during this period, the Russian state sought to use Tatars (who speak a language very close to Kazakh and had been part of Russia since the late 16th century) as a means to exert a greater "civilizing" influence over Kazakhs. Kazakhs were mostly Muslim in name only (if not tengrist animists), and the Russian state thought that Islamizing these peoples via the Central Spiritual Administration set up in Ufa in 1788 would settle them down and allow another level of state control. This period saw the establishment of Tatar-organized mosques and religious schools, as well as frontier courts (Tatar would be the language of administration in the region until 1870). Institutes of higher education (in Russian) were established for members of the Kazakh elites, which began an elite-level process of Russification. Russian military academies were likewise open to Kazakhs. Shoqan Valikhanov, a descendant of Ablai Khan, friend of Dostoeyvsky, and Kazakh author, attended a military academy in Omsk and was a member of the Siberian Cadet Corps, to give a famous example from the mid 19th century. Russian state policy in this period also encouraged Kazakh pastoralists to take up full-time farming through means like grants of seeds.

This also saw the steady split-up of the Little Horde and Middle Horde through ineffective leadership and interminable conflict (population increase drastically reduced herd size and the availability of pasturage, which fueled conflict). By the 1820s, a seemingly endless cycle of civil conflict, raids, rebellions, and Rusisan punitive expeditions had led to Russia abolishing the position of Khan in the Little and Middle Hordes, and their absorption into the Russian governmental structure of Orenburg and Siberia respectively. Mikhail Speransky, the Russian legal reformer, established projects to codify traditional Kazakh law (adat), which he saw as the best means to enforce order on the region. This legal system was gradually put into practice in the 1840s and by 1854 a military court system was set up to administer justice under these laws.