We got our camping permits at 12:01 am, four months ahead of the date. By 12:02 am, most of the sites were taken.
For multi day trips, you need to do that for each night you need a campgrounds. When you reserve day one, I added a comment that this was day 1 of a 3 day trip. The next two days, a similar comment (2 of 3, 3 of 3, etc). The park service will join the multiple reservations into a single reservation, and a single fee.
You have to confirm the reservation between 7 and 14 days before the trip date. If you donít confirm, they will cancel your reservation and open the campsite. So at times you can get a site up to one week in advance, but it is a gamble.