Summarize:

In some cases, marriages will be followed by an announcement in a local newspaper or newsletter. This is certainly becoming less common than it used to be, but if you are lucky, you may find a wedding announcement this way. Some obituaries also contain information on the person's marriage. If possible, you should start by finding where the marriage that you are interested in took place. This will allow you to identify any newspapers that may have published the date. If you know where the person was married, you can try looking on the website of the local newspaper in that location. Do a search for the names in the announcements section or public records section. Some larger local or state newspapers may have an online archive service, but you may have to pay to use this. You can find further information on online newspaper archives on a state-by-state basis here: http://www.neh.gov/us-newspaper-program. Some local newspapers may not have very thorough online records, so in some cases you may be required to visit the local library to see archive copies of the paper for the period you are looking at. You may also be able to search for the records at the newspaper's headquarters. You can find archive copies of newspapers in good public libraries, and access should be free of charge in most cases.
Learn the location of the marriage. Go to the local newspaper website. Go to your public library.