An authoritative source is one that has been written by an expert who is recognized in his or her field of expertise; some examples include peer-viewed journal articles, government websites, public records and books by reputable, well-known publishers. Some sources to look for are those that contain complete first-hand accounts of an event that happened and lack a one-sided view.
Another characteristic of an authoritative source is that its information is up to date. Verify whether the source itself can be backed up with other sources, what kinds of credentials the author has and the overall purpose of the work. Examining the purpose of the work is especially important when people use websites as sources because some websites are designed for the author to sell a product rather than provide balanced facts.