Woohoo, a question I can (sorta) answer.
I just shot my first HP match a couple weeks ago, so I can give you a basic rundown more or less of how everything works.
There's a few different courses of fire you might shoot. One's the national match course which is 50 shots, with ten shots slow fire offhand, 10 shots rapid fire sitting from standing, 10 shots rapid fire prone from standing, and a 20 shot slow fire prone. Distances vary depending on how far the range you're going to has to play with. Provided the space, it'll be 200 yards, 300 yards, and 600 yards. There's the 80 shot regional course match, which is 20 shots slow fire offhand, 20 shots sitting rapids, 20 shots prone rapids, and 20 shots slow prone. Plus or minus sighters for both courses (does the National Match course get sighters?)
Since you're talking M1As and Garands, I assume you'll be shooting service rifle. The only optics allowed are binocs or spotting scopes to check your targets downrange and read the wind and mirage. High power is shot with iron sights, be it a match or service rifle.
First time out, I'd call or E-mail the match director a day or two in advance and let 'em know you're new. Then show up about an hour or so before firing begins, so you can go over range procedure and whatnot. All you really need is a safe rifle, ammo, magazines or clips(I took five with me; kept four to use for the rapid fire strings that I reloaded in between relays, and one unloaded for slow fire), and a sling. Take heart in that high power shooters are probably about the nicest shooters you'll ever meet. For the most part, they'll bend over backwards to see that you have a good time and learn something about yourself and your rifle. Depending on how many folks are out there, there might be enough shooters for more than one relay, which means that you'll probably have a spotting scope and a mat you can borrow between relays. Be sure to check with the match director well in advance of the match.
Show up to watch? Good luck, heh. I showed up to watch about a year ago and guys were ready to loan me their rifles to shoot! High power is something you gotta experience rather than watching.
Again, all you really need is a positive attitude, a safe rifle, ammo, magazines or clips, a sling like a cotton Garand web sling or a leather 1907 style sling and yourself. Depending on how many relays there are, you might want to fix up a cooler with some water and lunch. A sweatshirt and a jacket, like a field jacket to soak up pressure from the sling, would help some too. It's hard, it's a lot of work, and it's incredibly fun and addicting.