Can someone please help me understand how to do an outline for my character analysis paper?
First of all, you need to choose which character you want to analyze, unless that choice has been given to you as part of your assignment.
Once you know who you are going to use for your focus, you need to get deeply acquainted with that character, the way s/he acts and why s/he does so, the influences that shape the character's words, thoughts and actions, and anything else that may be relevant. As you start identifying characteristics that you may want to mention in your analysis, also note examples from the book that support the importance of those characteristics.
For example, if you were writing about Governor Bellingham, you would explain that he was English by birth, but came to the colony and became very important there. Not only was he elected to be governor of the colony for some years, but he served as a judge, a "stern magistrate," during many other years. As a judge in a place where "religion and law were almost identical," Bellingham held great authority in determining Hester's future. His involvement, how it affected him, why he did what he did in the ways that he did - those are the kinds of topics that should be listed in your outline.
Begin with the most outstanding characteristic of your person as the first main point of your outline. Under that point, provide one or two illustrations of that point. Go on to the next characteristic you want to highlight, which becomes the second main point of your outline, with support for that idea listed under it. Keep adding major characteristics and examples related to them through the rest of your outline.