If you do not have a family story, a family bible, or an obiturary, then the next best place to look is in a marriage index.
Online marriage indexes:
If you are unsuccessful using marriage indixes, then you could try census records. Census records, at best, can give only an approximate date. When that is the case, the marriage year could vary by a year. U.S. Federal Censuses for 1850, 1860, 1870, and 1880 had a column to indicate whether the person had married within the year. So, there is a chance your ancestor did. But for most of us who had ancestors living at the time, this is pretty inadequate since it covers only ten percent of the possible years. The 1900 and 1910 Federal Census asked the number of years in the present marriage. That is pretty good and may vary by only one year. The 1930 Federal Census asked for the age at first marriage.
If your ancestor's marriage date is not in a census, then you could calculate an approximate marriage date based on the year of birth of the first born child in the census. Since most government agencies will search a range of years, that might work for you.
Once you have a marriage date, you can request a marriage record. This may be online, but if it isn't, then you should contact the county or state depending on if or when the state started keeping this information at the state level. If you do not know the exact year your ancestor married, most government agencies will search only a ten-year period for each request. So it would be good to narrow the time period at much as possible before requesting a search.
If you are not sure that searching for a marriage 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.