Look further than just the family or person you want to identify on a census record. If the family is listed at the top of a census page, look back one page to see if there are other members of the family enumerated as well as looking at the next page if the family is enumerated at the bottom of the census page.
Naturalization is the process of becoming a citizen. It is a two step process and takes about five years. The Declaration of Intent (1st papers) can be filed after two years of residency. Naturalization and Oath of Allegiance are taken after an additional three years of residency.
Look at case studies other family researchers have compiled to find similar cases to your family research. The trials of others often will give you clues for how to proceed in your family research.