I though it might be worthwhile to share my experience in getting a permit for a multiday hike in Paria Canyon. My wife and I are going with a buddy of mine in May. To get right to the point, getting a permit for any one month is a race, not a lottery.
I studied up on the permit process on the BLM website. It was clear that the calendar for the month of May would open up at 12:30 PM on February 1st, but it wasn't at all clear to me which of the two options above was right. So a few days ahead of time I called the BLM office and asked point blank if it was a race or lottery. I was told it was a lottery. Then, since you give credit card info and agree to pay in advance, I asked if it was treated as an application fee or a permit fee, i.e. if I don't get the permit do I still have to pay some or all of the fees? The guy on the phone couldn't answer that, bounced me to someone else who didn't pick for 5-10 minutes, so I gave up.
If it was a lottery as I was told, I planned to apply for four different start dates to increase my chances of getting a permit. I would assume that they would take all the applications for a given start date, randomize them somehow, then take the top one off the pile, award as many permits as requested, and repeat until all 20 slots for the day were filled. That's my understanding of how the do it in Yosemite. In which case I would only have to get my applications in early in February and I would get the result some time later depending on how long it takes them to sort the applications and award permits.
But, just in case, I decided to play it as if it was a race. I actually practiced filling out the form (without sending it in) for an open date in March so I would know what info I would need. Then on February first at shortly before 12:30 I went to the application web page and started renewing every 30 seconds or so until the calendar popped up. I clicked on our first choice date, filled in the info as fast as I could (thank God for autofill), sent it in, and went back to the calendar to go for the second date. But as I was filling that out, and email arrived saying that I had already been awarded a permit for the first application!
By 12:15, maybe earlier, pretty much all the slots in May were taken.
From all this I deduce that permits are automatically awarded by computer on a first come, first serve basis, making it a race to see who can fill out an application fastest for any given date. Fair enough, but it could be a lot clearer on the web site. If you really want a Paria permit in any of the high demand months (May, September, or October by my reckoning) then you should do what I did: line up at the starting line right on time.
I know people like to grumble about having to get permits for access to public land / wilderness, but the good news is that, once you get one for one of these super popular backcountry places, you won't be dealing as much with the hordes of people and resulting overuse impacts that you would get if it were unregulated. OTOH there are 600 people a month going through the Paria in high use months, and if I guesstimate that on average people do it over three nights (we're taking four, some do it in two) then that would be about 60 people camping somewhere in the canyon every day. That does seem like a lot of use -- I guess we'll find what it's like out first-hand when we do it in May.
Day use permits are unlimited and you can get them at the trailhead, so you can do shorter hikes without all the competition. My wife, daughters and I did the 20 mile hike down Wire Pass and Buckskin and back up the Paria as a long day hike in June 2011.
Anyway, learn the rules, play by them, and you'll probably have yourself a good time.