First you ask Marriott to make you an offer for renting your week. They will respond with an offer, if they want your week, within a week or two. If you choose to accept Marriott's offer, you return the signed agreement and you'll get a check within another two weeks or so. That's all there is to it.
To rent with Marriott, you must offer Marriott your entire unit, not just a portion of it.
If you choose not to accept Marriott's offer (or if Marriott doesn't make an offer), you can use your week, deposit it with II, lock it off and use part of it and deposit the other part with II, deposit both parts as separate deposits with II, deposit it with an independent exchange company, rent it yourself, or, assuming you bought from Marriott and meet the requirements (including deciding before 12/31/06 if it's your 2007 week), you can exchange it for Marriott Rewards points.