I've umpired off and on for the past 10 years or so. Do it whenever you can, at every level you can. The more experience you have when you go to those camps, the more you'll get out of them. You'll also come across tricky situations more often. I've never gone to camp, but I do it more as a fun hobby that puts some extra money in my pocket.
Being an umpire is also much much more than knowing the rules. You have to be able to make a quick decision, be able to not take it too hard when you blow a call (you WILL blow calls), and be able to take some tough criticism from coaches and (especially nowadays) parents. I once even had a 4th grader tell me to get my head out of my ass after I ruled his home run ball foul (the foul lines were moved the previous season, but they kept the poles up, so I'm still not sure what foul pole I looked at when I ruled).
Also, keep in mind that it's harder to become a professional umpire than a professional ballplayer. There are such limited slots, and (unfortuntely) a lot of what I've come across has shown me that you need to know the right people to get the good jobs. I know only a few of the right people, so I usually get stuck at the 6 inning games that take 7 hours where nobody can throw strikes.
EDIT: I forgot to answer your original question. Call the local leagues or show up at their games. I guarantee that they are short on umpires, and could use the help. That's how I got started, and everybody seems to know everybody. In my busiest summer, I'd do a different league every weeknight, and two or three games on Saturdays. Pay was based on level of play and whether or not you were behind the plate or in the field.
Also, I'd buy my own gear. I bought shinguards, a mask, a chest protector, umpire shoes (though they can be expensive), and (most importantly) a cup. Most catchers can't catch if they're under the age of 12, so be careful.
I have a buddy that just quit being a MiLB umpire right after their work stoppage. He started umping while he was in high school, doing little league games, and worked his way up to doing Babe Ruth and HS games by the time he was a senior in HS himself. He started doing HS games every year, and even worked a few D1 college games in addition to regularly working Juco as well. I forget which umpires school he went to (it wasn't Wendlestedt's), Laz Diaz is affiliated with it, but it's my understanding that your best bet to get on with MLB/MiLB is to go through one of those schools. He had worked his way up from Rookie ball to high-A over the last few years. Be prepared to not be paid very well, however, once you get into the league.
But yeah, contact a local high school coach, and find out who organizes the umpires in your area. Get in contact with your local little/Babe Ruth/American Legion/Adult Leagues, and tell them you want to help.
They want to deliver vast amounts of information over the internet. And again, the internet is not something you just dump something on. It's not a truck.
The Detroit Tigers defeated the Chicago White Sox 4-3 today, thus ending their chance at a perfect 0-162 season. And I thought this was going to be their year. Of course, they couldn't have done it without the White Sox blowing several scoring situations....