Most of us use trainers who specialize in eventing (though that, of course, means they have solid backgrounds in dressage and jumping, and often we go to dressage or jumper shows to tune up those phases). I find that as riders/horses move up the levels, many start to also work with a dressage trainer especially (in addition to their eventing trainer). For getting your feet wet, though, just an eventing trainer is the way to go, as s/he will be best equipped to help you understand the cross country, the rules, the competition, and what to do when you are at your first events!
Most people don't want to jump (no pun intended!) straight into recognized events - they're bigger, more expensive, and less appropriate for schooling - so I'd also check out the unrecognized events in your area. The Area IV website has a list of unrecognized events (as well as other useful info), and I would also check any local equestrian newsletters, magazines, or websites that list competitions. Of course, once you find an eventing trainer, that person will be able to point you to appropriate venues, as well.
I use two different trainers -- one for dressage and one for jumping. However, both have evented in the past (one at the highest, **** level and one at a lower level but rode Prix St George dressage). I find I like the dressage expertise separate and more specialized, she seems to offer more of a gradual approach of building blocks while still understanding the needs of the eventing horse.
I've been looking around at other disciplines, as I've finally gotten a bit bored with going around in circles....
Sigh even my AOTR alter ego is switching to the dark side. I guess this sort of justifies my present urges to just go galloping through the hay fields and jump ditches and logs. But, now who will I go in circles vicariously through?
Why is it that a woman will forgive homicidal behavior in a horse, yet be highly critical of a man for leaving the toilet seat up?
~ Dave Barry
Good advice in previous posts. Prob easiest to have one coach for all disciplines, particularly at lower levels, but not required. Find a friend to share experiences with, eventing no fun alone. Volunteer at an event, and hang around the barns to meet people. I've never been to an event I didn't meet a new friend.
I'd suggest contacting Illinois Dressage & Combined Training Association at www.idcta.org - they'll be able to put you in touch with local trainers & other eventers in your area. Also try USEA Area IV at www.usea4.org for a list of Instructors.
Brock n. (Anglo-Saxon) badger as in Brockenhurst, Brocklebank etc www.area35.us