Berry Benson was a sergeant and his memoirs have been published.
Marion Hill FitzPatrick was another non-com whose letters have been published. Unlike Benson he died (at Petersburg).
John Worsham was another enlisted man.
Sam Watkins, Company Aytch, also published his memoirs post-war.
Wyman White of the Second Berdan Sharpshooters was a non-com and his diary has been published.
Corp. Norman Shepard's (146th NY Vol.
Inf) memoirs have been published.
There are hundreds of other memoirs that have been published. Each will describe in some detail the duties the soldier experienced as a non-com.
As to qualifying for sergeancy, being liked by the officer(s) weighs heavily. Last man standing is another rule. Sometimes it is a very senior private who is trusted and respected by his officer. In newly formed units, it could be that the person learned the drill from an earlier and now disbanded unit. His valuable experience made him eligible (sometimes even for an officer's commission).
There is more pay and like today, it goes up according to the rank. How much more I never bothered to notice.