Most first drafts of SOPs I've seen start with a narrative of the person's past and background, and only get around to their current/future interests towards the end of the essay. To have a good SOP, however, the focus should be on your current and (mostly) future research plans, and it should be apparent what your interests are as early as possible. It's the same advice I get now for writing papers - don't recount the history of all your failed attempts and bad starts, tell me the path that succeeded and show me what you can do with it.
For a good, focused SOP, you should be able to demonstrate that you are familiar with the inner workings of your field. Address strengths and weaknesses in current thought about your topic, or suggest a fresh way of looking at it; choose a project that is feasible in size for the degree you're applying to; aim to have similar interests/methodology/both as the researchers in the department you're applying to. Remember that you're not committing yourself to actually doing the project, you just want to show the adcom that you can think through the details of a possible project within your area of interest. Choose no more than 1-2 interests as your main interests and spend most of your time talking about them. It's OK to have secondary interests, but it should be clear where your interests lie.
Aside choosing the right kind of interests to discuss, fit is also understanding your intended department's attitude towards things like collaborations, innovation, going in unexplored directions, doing quantitative/qualitative/theoretical/practical/etc work. Talk about things that make sense for that department. Mention anything unique that the program offers - resources, reading groups, any kind of opportunity like an exchange or a diploma. If it's not a school that emphasizes teaching, don't dwell on that. If you're not sure that you'll be encouraged to take courses at other departments, make sure before you mention "resources" that are not really going to be there.
If you want to mention coursework in more detail, most applications will allow you to e.g. upload a summary as a supporting document or as part of your CV. You can also attached it to your transcript. Include a list of course names/numbers, the instructors, and a one-paragraph description of each course (+optionally, the grade and nr of credits, but that should be on your transcript; optionally2: the topic and short description of term papers you wrote for each course). All those details don't really have to be in your SOP, unless they're directly tied to your current/future interests. If you've caught the adcom's eye, they'll go look at your credentials anyway. Optionally: give a link to a website that contains all the work you're comfortable with the adcom seeing. It can be a simple googledocs-based site, I hear they are easy to make. If they're really interested, the adcom might want to know more about your work, and that's a great easy way to give them that extra information.
