We have several years of sponsorship under our belts, so peaking from that, here goes.
The website is the place to start for prospective sponsors. If you have family within the XX mile limit (used to be 22, now might be slightly more, someone will have to help here), they can apply. They will have to attend a briefing session, and there are usually a handful of times to choose from. Usually one person is the sponsor, so ensure you have that name down before you come. They put your name down, you put theirs, should be a match. Not sure what the forms on the Plebe end look like now, but you can usually indicate no animals (allergy issues), no kids -- some choices there.
Even if you think you don't need/want a sponsor, do it -- it's a way of getting off the Yard and enjoying some time in a home. And, just about the only people you are allowed to ride in a car with are family, sponsors, officers, 1/C sponsor siblings and a very few others. We have remained very close to all our sponsor alumni. We have also adopted many whose sponsor situation didn't work out. It's a great program, and there are lots of experienced and caring sponsor families.
There is a Sponsor Social, usually on a Sunday or Saturday afternoon, in Alumni Hall, the weekend before PPW. Almost works like "Come on down!" on Let's Make a Deal. Sponsors check in at the tables and are given a print-out of their assigned sponsorees. Plebes will be sitting in company groups, and sponsors circle around and ask the 1/C in charge of each group for Plebe W. T. Door. (if you don't know who what is, you'll know in about a month) Plebe Door comes on down, meets sponsors, and there's about an hour to chat and swap info. We always bring along a briefing sheet with contact info and other key stuff they can share with parents in the next designated phone call.
Visiting sponsors occurs during periods of town liberty, as well as leave. We've had several orphans over Thanksgiving and in between summer training blocks.