Spending a little time in researching these societies can be quite fruitful as they can give you clues to the status or standing of your ancestor in the community. At first, you may have nothing more than family legend to document your ancestor's place in a fraternal organization, but once you know where to look, the search should become easier.
One place to begin your search is at the local cemetery. Often the tombstones of fraternal members have symbols that are quite ornate. There are a few places on the Internet where you can search for pictures of these symbols to compare against your ancestor's tombstone.
Another place to look that may yield some clues is in your ancestor's obituary, if you have it. If you don't, it may be worth checking with your state archives for copies of the local newspaper that might have printed the information at the time of death. Very often, membership in fraternal societies is mentioned in the obituary.
For Union soldiers of the Civil War, a very special society existed called the Grand Army of the Republic or GAR, which was formed to honor men who had fought for the Union. Records from the GAR may exist in state archives, so it is worth taking a look. Records may also exist in the state archives for other fraternal organizations as well.
Some fraternal organizations were formed based upon a person's occupation. Railroad fraternal groups may allow you to identify which railroad your ancestor have belonged to. Knowing which railroad makes it easier to collect information about the railroad as it was in your ancestor's time, allowing you to paint a picture of their everyday life.
If the fraternity is still active, you may inquire of the local branch as to the existence of old records and how you might have access to them. Your request to access the records could be denied, but it never hurts to ask.
Taking the time to search for information of your ancestor's link to fraternal organizations can provide great clues to their lifestyle and perhaps will give you a piece of the puzzle that you have been missing.