One of the problems writers have is that we tend to speak in fragments frequently, a kind of shorthand that works well when people are face to face or know one another well. It is in writing that the fragments become a problem, largely because your "ear" does not detect what is missing.
As you proofread a paper, each group of words that begins with a capitalized word and that ends with a period must have a subject, what in the sentence is performing an action, and a verb that is the action the subject is performing in the sentence. If you ask yourself whether the reader can tell what or who is doing something in this group of words, and if you ask yourself whether the reader can tell what that someone or something is doing, you can spot a fragment if the answer to either or both questions is "No."
Some people have a hard time with the verb "to be" because there doesn't seem to be much "action" in a sentence like, "She is the mother of three." But in that sentence, "is," a form of "to be" is considered an action because the subject is being someone.
Identifying fragments or avoiding them in the first place is something that anyone can learn to do with a little practice, as long as you understand what the basic requirements are for a sentence.