In order to locate a naturalization record, you need the state your ancestor resided in at the time. If you do not have that information, you can determine the state where your ancestor resided by searching census records. Also, the 1920 Census asked for the year of naturalization. More on census records.
Another source for state of residence is an obituary. Sometimes an obituary will include when and where a person resided. More on obituaries
Naturalization records are generally available from state archives or historical societies where your ancestor resided at the time of filing naturalization papers. Often, these archives are indexed and can be searched by name. The website where you searched the index should also have instructions on how to obtain a copy of the naturalization record.
If you know your ancestor moved from one state to another, then it is possible that first papers were filed in one state and second papers were filed in another. You will need to search for naturalization records in both states.
Online resources for naturalization records:
If you are not sure that searching for a naturalization record is the next best option for your research, consider using the advice feature of this site. This will help you pick your next best steps in your research. Go to Genealogy Search Advice.