Read through the definitions of authority given by the dictionary.
Here a few characteristics that build authority:
Different types of authority:
Look over one of your sources, and select one that is of interest to you. Look at your source, considering these questions:
You get to be an authority yourself. While you're reading something, take notes. What are their qualifications? Are the experts' claims backed up by evidence? Do the points they are making seem to follow logically?
Keep in mind, expertise is usually specialized & narrow. An expert in one area is not usually an expert in all areas. It makes a lot of sense when you think about it: most experts specialize in one field, because of the time and energy it takes to engage deeply with a certain subject. It's the reason that a hospital will have someone who specializes in brain surgery and someone who specializes in heart surgery.
So, keep asking yourself: What makes this person qualified to speak on this topic? Are they respected/trusted by other experts?
Find some kind of article, item - what kind of authority does the author have? Any credentials listed, where is it published (affiliations), is anyone else citing this.
For example, look at the two links below referring to David Robert Grimes.
Who is the author?
What are his credentials?
Where is his work published?
Where does he work?
Has anyone cited his publications?