Focus on the first sentence. Read it out loud as if you were reading it for the first time. Ask yourself whether you would continue reading if you were reading about someone else. If the answer is no, revisit the sentence. Consider adding variety to your sentence structure and adding unusual verbs to draw the reader into your story.
Read the first three words of each sentence in your narrative. If every sentence starts the same way, then you need to make some changes. In a personal narrative, it is tempting to start most sentences with "I". Resist this and make changes to the beginning of your sentences.
Evaluate the topic. Is it interesting enough to write about, and does the story provide enough detail to interest the reader? If not, look at your descriptive words, especially verbs. Try to use different words with similar meanings, instead of repeating the same handful of words over and over. This will bring more variety to your narrative and influence the reader to continue with the story.
Review the order of the narrative. Whether it's chronological or organized in some other way, it needs to make sense to the reader. If you randomly jump from one scene to another the reader is likely to become confused and disinterested.
Write the narrative for your target audience. If the paper is for a class, then a certain amount of formality may be necessary as compared to a blog or other personal article. Also consider the perspective of the narrative. Would the person who's perspective you are writing it from know the things you are writing about? Make sure the angle is believable.