Go searching on the www and you'll probably find lots of ways and formats to write a series proposal. One thing I learned when putting together a proposal for the Charlie Madigan books (after I signed with my agent), is that there's no written-in-stone formula. But there are a few things that usually make up a proposal.
Let's look at the writer persuing representation:
When you submit a fiction query (and you had better have that book completed and polished, and polished some more. Trust me on this, k?) and an agent writes back asking you to send a proposal -- it usually means a cover letter, the first three chapters, and a synopsis. (Some will also ask for a bio). Even if you plan your novel as a series, you don't want to send anything other than what the agent asks for at this point (although, including the fact that this is a series is perfectly fine in your query or cover letter). If the agent wants to see additional info, after reading your initial proposal or full ms., they'll ask.
What should the length of your synopsis be? Good question! I can only say it differs. 2-3 pages, all the way up to 10 or more. My synopsis for TBPD was 2 pages. My synopsis for Book 2 was sold based on a 3 page synopsis (and the strength of a completed Book 1).
When you already have an agent and want to present a new series idea, you might (or not -- depends on you, and your relationship with your agent) first talk about it to see if it's something worth persuing. Either way, you write the first three chapters and synopsis -- your proposal. And you might also write a short synopsis on additional books at this time, or wait until your agent is ready to submit to editors and wants to include them for a possible book deal. But, let me just say here (disclaimer!), every agent is different in what they prefer to see from clients, and what they ultimately decide to send out to editors. For some, a synopsis of additional books, or simply a story arc showing how you envision the overall series can be a good way to clue your agent in on your vision. And it might help them devise a plan of attack and advise you -- is this series commercial? Is there a market for the books? Has something just like this sold recently?
So, when I write a series proposal, it consists of the first three chapters, synopsis, and then my overall story arc for the entire series, which ends up being anywhere from 6-12 pages. This is also a good way to get an idea down 'on paper' and out of the way, so you can continue to work on your current/main project. I did this over the summer -- had an idea that would NOT leave me alone, so I wrote the proposal and a lot of notes and then set it aside.
This brings us to the point where I wonder if I even answered Christine's question, and where I realize that I'm mostly rambling now . . . :D
Questions? Just fire away..