Many of our ancestors came to the United States with the intention of never returning home. They had left bad times behind and were going to a new future. Part of this meant becoming an American citizen and cementing their role as Americans.
Naturalization was a two-step process so there are two sets of paperwork for most petitioners.They first filed a declaration of intent after two years. After three more years they could file a petition for naturalization. You really want to see both pieces of paper if possible since one or the other may contain more information.
Information that you can expect to find on naturalization records includes ancestor's names, birth place, port of entry, date of naturalization, location of naturalization, ship name , names of family and friends. However, the information in some states is much more complete and useful than in other states.
Family Search is in the process of indexing and digitalizing naturalization records. Not all of them have been turned over and you may have to go look into the local courthouse to find your ancestor's naturalization. To determine if they were naturalized, you can go to the 1900 census and they were asked if they were citizens.
I was able to locate the index cards for two of my ancestors in the Family Search database. Keep in mind that woman of this time period would not have been naturalized, she had the citizenship of her father or husband.
Family Search is also looking for volunteers to help get the information searchable online. Go to their website for more information.