Russian imperial expansion takes two stages that are distinct in the apporach and in the people living in the areas, so I'll break that up. First is the Kazakh steppe, which is essentially the land of modern day Kazakhstan. People lived nomadically here and the Russians really took the land in the early-mid 19th century. Second is a push into the cities of the region, most notably Tashkent, Samarkand, Khiva, and Bukhara.

Before Russian expansion into the Kazakh steppe, life was nomadic. Nomads were generally herders and would practice transhumance, or moving with the herd depending on the season e.g. north in the summer and south in the winter. Tribes were patriarchal, and were at least nominally Muslim. People still held onto many animist beliefs such as ancestor cults. Islam was much weaker in the nomadic peoples than in the sedentary populations in the cities as it's pretty much impossible to set up schools and institutions while constantly traveling.

Kazakh Steppe

Ethnically the people living in this area were Kazakh (hence Kazakhstan). Politically, they were divided into three groups: The Little Horde which had control over the western parts, the Middle Horde in the middle of the region, and the Great Horde which controlled the eastern side of the region. These people would trade with Russia and even signed some treaties with the Russian empire. These treaties get complicated as the nomadic people view them as temporary, while the Russians did not. The Russians would use these treaties as a way to take land and extend their influence, building forts along the way.

This section of the Wikipedia article has some very nice maps that help show the advancing line of fortification. Omsk was built in 1716 and Semipalatinsk in 1718, which really helped secure the area for the Russians at that time. Treaties were signed between the Russians and the Little and Middle Hordes from 1731 to 1742. Russia originally used these to gain political influence (they were giving military assistance to the Khans and used this as leverage), and eventually annexed the territory. There were some revolts, most importantly some parts of the Pugachev rebellion which was one of the most successful rebellions against the Russia Empire. However by the mid 19th century, the area was under firm Russian control.

The Russian Empire followed through with their civilizing mission and forced many nomads to settle down and become "civilized." Forced settlement, taxes, and reduction of pastoral land dealt a heavy blow to the Kazakh way of life. Russian settlers began to move in, taking the best land for farming, and further reducing the space for nomadic travel and herding activities. In an interesting twist, the Russian Empire did not try to Christianize the Kazakhs, but actually tried to strengthen Islam among them. The idea was that though having Muslims in an Orthodox Empire could be an issue, pagans were even worse. The Russians brought in Crimean Tatars to help spread Islam among the Kazakhs.

Cities

Second is the southern advance into the large cities. Tashkent fell in 1865, Khiva in 1873, Kokand by 1876, and the rest of Central Asia by 1884. This also stirred up animosity between the Russian Empire and the British Empire known as "the Great Game." The British thought that the Russians might try to take India by moving through Central Asia and were very worried (not that this was all that feasible, but the British were afraid). Dr. Watson of Sherlock Holmes fame got his wound in 1880 in Southern modern day Afghanistan, which helps to show how close the two Empires were. Eventually some treaties were worked out between them.

Politically, Russia generally controlled the area with indirect rule which gave the local leaders a great deal of autonomy. These leaders were largely authoritarian and did what they wanted as they were protected by the Russian Empire. The Russian Empire required that the cities were opened to Russian merchants, and that the slave trade was outlawed. Reparations were also required to be paid. Like in the steppe Islam was actually reinforced under Russian rule. This was generally to maintain stability in the region.

As for life at these times, one of the best accounts is from Chokan Valikhanov in his Chinese Turkestan and Dzungaria in The Russians in Central Asia (available for free here). Chokan was an ethnic Kazakh, and was the grandson of the last khan of the Middle Horde. Dzungaria is essentially the north-west of modern China. Chokan gives a good account of the daily life of the Kazakh (he calls them Kirghiz, but they are actually Kazakh) peoples that he meets. He says that they are a very dirty, talkative, and quarrelsome people, but (at least in my reading of the text) he goes to great lengths to say how welcoming they are. There are some great quotes like "our host was extremely civil, though he frequently cursed the tombs of our fathers, apparently only from force of habit" (79). Though he was outside the cities, he traveled in the 1850s/60, so I'm including it in this section.

The Russians also began lots of work to start cotton farming in Central Asia. Adreas Kappeler notes in The Russian Empire: A Multiethnic History that "Whereas in 1885 cotton had been planted on only 14 percent of the cultivated land in the Fergana valley, by 1915 it was already approaching 40 percent" (198). There were also many irrigation projects as well.

I've basically tried to take an entire class that I've taken and squish it down into this, so please let me know if you want more information or clarity on any of this, or if you have any questions I didn't address.

Sources:

Andreas Kappeler The Russian Empire: A Multiethnic History WorldCat

Valerie A. Kivelson and Ronald Grigor Suny Russia's Empires WorldCat

Chokan Valikhanov Chinese Turkestan and Dzungaria (Google Books link above)