Aleksandr Solzhenitsyn establishes this important theme of friendship right from the outset of the novel. He first brings up the theme of friendship while establishing Denisovitch's characterization and the conflict:

Time to get up. ... Too cold for the warder to go on hammering. [...] Shukhov never overslept. ... [He could] ear a bit on the side. ... Not today, though. Hadn't felt right since the night before--had the shivers, and some sort of ache. ... Kept hoping morning would never come.

In the midst of establishing character and conflict, Solzhenitsyn brings in the theme of friendship. The narrator points out that it was friendship that allowed Denisovich to learn the means of survival when he first arrived. An old-timer at the camp, Kurzyomin, allowed Denisovitch into his favor as he gave advice around a campfire when Denisovich first arrived and instructed him that it was possible to live at the concentration camp, as it was possible to live virtually anywhere, if a person paid careful attention to the simple rules of survival. This is a demonstration of friendship and lays the course for further development of the theme as the narrative progresses:

[Kurzyomin said] "It's the law of the taiga here, men. but a man can live here, just like anywhere else. Know who croaks first? The guy who licks out bowls, put his faith in the sick bay, or squeals to the godfather."
    He was stretching it a bit there, of course. A stoolie will always get by, whoever else bleeds for him.

One way in which the theme is further developed in the rest of the narrative is through the efforts prisoners put in on another prisoner's behalf. For instance, when the Tartar warder sends Shukhov to the hole, regular work hours (half punishment), for not getting up when the hammering sounded, the narrator (third-person limited, though so closely associated with Shukhov that it feels like first person) explains that the foreman of Shukohov's gang would have put in a good word for him and suggests that all his gang members would have liked to put in a good word for him (and maybe get him off punishment) but knew it would do no good, not through defeatism, though that effected them, but because they knew it would do no good.

All the men in Gang 104 saw Shukhov being led out, but nobody said a word: what good would it do, whatever you said? The foreman might have put in a word for him, but he wasn't there.

What are examples of friendship in Solzhenitsyn's One Day in the Life of Ivan Denisovich?

In my opinion, the theme of friendship is prominent in Solzhenitsyn's novel One Day in the Life of Ivan Denisovich. In fact, Solzhenitsyn starts with this theme right away.  Desperate at the beginning, Ivan depends on his memories of friendship in order to learn the skills of survival.  Where he would have found despair, now Ivan finds the will "to get up" further adding that he "never overslept." 

A second example has to do with the character of Kurzyomin.  Kurzyomin was the first to establish friendship with Ivan as soon as he arrived at the concentration camp.  How did Kurzyomin do this?  Simple: by telling stories around the campfire and giving Ivan words of advice.  Kurzyomin has lived at the concentration camp a very long time.  As a result, he knows the drill.  Put simply, Kurzyomin knows how to stay alive and wants to share that "how" with his new friend.  What was this important advice shared around the campfire?  To follow the rules and live at attention.  Make survival your ultimate goal.

A man can live here, just like anywhere else. Know who croaks first? The guy who licks out bowls, put his faith in the sick bay, or squeals to the godfather.