Look at the sentence fragment in question. Read that portion without any of the previous information that may be provided. If the sentence tells a story in and of itself, it is probably fine. If the idea must be developed further, it is probably a fragment. By rewriting the sentence to include an entire idea, you can correct its fragmentary nature.
Find the subject and the verb in the sentence. The verb tells what the subject does, or is doing, or has done. In order to correct sentence fragments, the verb plus the subject must be joined in a completed action. In a very simple sentence such as "I ran," "I" is the subject and "ran" is the verb.
Rework the sentence fragments so that each one is a complete idea on it's own and needs no further explanation.
Review proper sentence structure to be sure you understand what makes a sentence complete. You can purchase workbooks in most grocery stores or you can find printable lessons online.