If you go to the ADS site, they have lists of clubs/orgs and usually those have their own events. I think there is also a list of ADS events. Oh, here is Celine's calendar for the Western States, it is very comprensive:
CVHA Calendar
I know the Pacific Regional Gathering has some lessons and stuff that allow minis in. Unfortunately the instructor I would recommend to you is totally filled up already(David Ventura), but you can audit for free(go watch and listen)...you will learn a lot.
A lot of the other things, I think probably allow minis, but I'm not sure on that. So you can email/call them and ask...most are very nice people!
The play day at RamTap allows minis(I have taken some), that is nice and easy going, basically you can just go play on the course, not org. at all. RamTap CDE lets minis in, it is an exceptional event, and it will fill up on the first day, so get your entry in on opening day. Pleasure Days is another 'definite' for minis. Mighty Minis CDE is not on there, but it allows minis too(duh!), that is in the fall of 06. And Oak Run HDT, in Feb., also allows minis.
As far as "how do they work"...I would recommend becoming a member of the ADS--they have a rulebook that explains everything, its cheaper for events, and you get a really cool mag.
CDEs are like eventing shows, only with cart attached and no jumps. The first competition is Dressage--there are 'rules' of dress(gloves, hat, apron, whip, conservative) and everything is perfectly turned out and clean. Then, Marathon(though if you are only doing a two day event, cones would be right after dressage), where you do a course(5-10 k for minis), with obstacles/hazards(go through certain gates in the right order), and you have to do this in a certain time frame. Last, is cones. Cones is a short(2-4 min. long) course, where you drive through pairs of cones, with tennis balls(or apples, LOL) on top. You get penalties for too slow and knocking off the balls(or killing cones).
Some advice: work on dressage...this is a good conditioning tool as well as good for your dresssage score. For training, work on rhythm, relaxation, attentiveness, and some submission(acceptance of the bit) and bending(on the curve of the circle). This is where it pays off to get your hands on dressage books, attend clinics, ask people, etc. If a horse is working correctly, it is harder for them than going 'down the road'--the bending and roundness at first is hard for the horse that is not used to using those muscles. Work up to around an hour, I've found thats about where my horses' best performance is, if I go until I reach that 'plateau'....if they are getting tired or frustrated, back off, and either unhitch and put up(end on a good note) or go for a pleasure drive. Dressage should be enjoyable for your horse, not a torture session.
Or you can mix ring work and out work....do 15-30 minutes of one thing, switch to the other, etc.
Good luck!