Every advisor has his or her own style and expectations. I've described mine here to help guide you in your choice of advisor for your philosophy independent work.
If you would like to talk to me about an independent work topic, the best thing to do is to see me at the very beginning of the semester. Stop by my office hour (listed on my web page) for a quick chat. There's no need to email in advance for this--just stop by during the office hour.
During our chat, I can advise you on whether the idea makes sense as JP or thesis, and on who would might be good advisors for it. If it makes sense for us to work together topic-wise, then most often you can just get started on thinking about and writing the paper after we talk. On some occasions I may be working with many other students already---if so, I apologize in advance if I have to ask to work with you in a future semester, or if I suggest alternate advisors to talk to.
Before we begin working together, please read the departmental information about JPs or Senior theses and Senior departmental exams. Among other information, these links also describe intermediate deadlines that I will expect you to follow. In addition to those deadlines, for JPs you should give me a substantial draft by Dec 1 (Fall term JPs) or Apr 1 (Spring term JPs).
It is important to leave plenty of time for revision at the end of the writing process. Seniors especially should be sure to give me any drafts by Wed Apr 18, so that in case there is important feedback, there will be time to think about things and make changes.
Once we are working together, I've found it most fruitful if you go off and think about things, then come by my office hour when you've got an argument or idea you want to try out, or when you get stuck. At the beginning you'll be nosing around in the literature to narrow your topic. I advise that you learn how to use "The Philosopher's Index" for this stage, which you can find (along with other good philosophy resources) on the library's Philosophy Resources page.
Later on, you will want to get feedback on your own arguments and lines of thought. The thing to do is to think through your idea and write some notes to yourself or an outline explaining it. Then bring those materials to your meeting with me and use them to explain the idea to me.
I expect my advisees to take advantage of the philosophy department's senior thesis writing group. It is led by a philosophy graduate student, and students have found it extremely useful.
It is important that you stay in touch with me about your thesis. Please stop by my office hour every once in a while, even if just to report that you're stuck or haven't made much progress. Sometimes I can help you get unstuck.
I can't help you if you don't talk to me. And I can help you if you do talk to me.
Sometimes students get behind and fall off the map. Don't fall into that trap. If you are feeling overwhelmed or behind, it is always easier to consult sooner rather than later. This is true even if you come into my office and say "I'm terribly behind and have done nothing". But do this early!
When you submit a revision of work I've already read, please send along a version with significant changes indicated. In other words, format in boldface (or other easily distinguishable way) those passages or regions that involve significant changes or additions. Don't worry about indicating every little change---just help me focus in on what important changes you've made.
Don't think of your task as planning and writing a book. Instead think of it as writing a short philosophy paper. And then a medium length philosophy paper extending or taking off from the ideas of the first one. And then another one. And perhaps one more. And then tying it all together.
In particular, I recommend that your first piece of writing not be a gigantic outline or introductory chapter or survey of any sort. Instead you should write a thesis bite. A thesis bite is a short (typically around 8 page) paper with a modest, well-defined aim. Think small and unambitious. The idea is to factor off some corner of your thesis question that admits of self-contained treatment. Set yourself a task that is not overwhelming.
Your thesis bite will probably end up being part of your thesis. But you needn't think of that when you're writing. You needn't think: this is section 1 of my master work. Think instead: this is a philosophy paper that clearly argues for a modest thesis, or accomplishes a helpful bit of explication of a hard text. Finish it and get it under your belt.
If you get stuck at this stage, it's especially important to see me right away. It may well mean you should shift your topic, or consult some other reference.