Every sentence should have a subject, a verb, and a complete thought to express. If you are missing any one of those elements, you are writing a sentence fragment.
Here are some other clues that you might have written a sentence fragment:
Does the sentence start with a subordinate (after, although, as, so that, because, than, before, ect.)?
Ex. After she walked down the road.
Does the sentence begin with a word ending in -ing or -ed?
Ex. Walking down the road.
Does the sentence contain an infinitive phrase (‘to’ + a verb)?
Ex. To walk down the road very quickly.
Is the sentence only an afterthought fragment (commonly starts with especially, except, excluding, for example, for instance, including, like, and such as)?
Ex. Excluding the tiger that I dreamed about.
Does the sentence begin with a coordinating conjunction?
Ex. And jumped really high.
Most of the time, if you just look at a suspecting sentence and ask yourself if there is a subject, verb, and a complete thought, you should probably be able to determine if it is a sentence fragment or not. The fix is just as easy — either connect two fragments or add in the missing information. A lot of those examples could be fixed by simply adding a subject.
Sometimes using a sentence fragment may seem tempting, but there’s pretty much no place for them in college writing. Save such experimentation for creative endeavors and remember: If you’re going to successfully break the rules, you have to know what they are first.