Brainstorm to discover a topic. Make a list of events from your past that have stayed in your memory over the years. Don't try to edit or analyze your list at this point. Simply put down the memories that come to mind. Chances are that if a memory has stayed vivid in your mind for all these years, it has some significance.
Choose a topic that lends itself to analysis. A memory paper requires that you not only describe the memory, but that you also analyze and discuss its meaning and importance. Look through the list you have created and pick a memory that fits these criteria. If no memory you have listed does this, add more memories to the list.
Determine the best way to present the event. There are several ways you can write about the event: as a flashback, where the narrative starts in the present and then moves to the past; in chronological order, where the narrative moves from past to present; or in reverse chronological order, where the ending scene of your memory is told first. Think about your specific story and decide which way makes the most sense. Does your audience need to know something about your life today in order to understand the memory? If so, use the flashback technique. Will a reader find the story more interesting if the ending of the memory is the last part of the paper? If that is the case, use a traditional chronological narrative.
Write vividly and make the scene come to life. Draw as many details from the memory as you can. Use adjectives and adverbs to describe the setting and the people involved. Realize that the audience knows nothing about the memory, so make it clear who the people are, where the memory is set and the course of action. Tell what the characters are thinking and saying, especially your own character.
Give your analysis of the memory. Tell why the memory is important and how it has influenced your life. This is often the most difficult part. Try writing the details of the event and then letting the paper sit for a day or two before you offer your analysis. This cooling-off period often makes it easier to understand the influence of the memory and to write about it.