Ask where they heard the story so that you can determine if they heard it from different sources. Ask questions to clarify any facts or points that are unclear. After you've obtained several versions of the story, examine the details and look for similarities and discrepancies. Similarities may be indicators of the veracity of the facts. At this point, it is important to try to locate evidence that substantiates details of the family story.
Documentary evidence is excellent.
For instance, my ancestor, Thomas Weatherly, was said to have been a drummer and fifer for George Washington's army at Valley Forge. I was able to corroborate this fact with Revolutionary War muster and payroll records and with pension application records, all obtained from the National Archives. In other cases involving less notable events, your research may involve the use of more mundane records such as deeds, tax rolls, voter rolls, and newspapers, as well as family letters, journals, diaries, and other family keepsakes. Your goal should be to locate any materials of any sort that corroborate or negate the facts as recounted in the family stories. It is important to document every facet of your family history.