Fortunately the hunter courses are the easiest to remember! (since you labeled this "show jumping" I was wondering if you were from europe and I have no idea how they do things there!) It's not like in the jumpers where you have to jump one fence, make a tight to another one, roll back... etc.
Here are some definitions you probably know, but just in case I'm going to put them here anyways so you know what I'm talking about!
Line- 2 (usually 2, sometimes more) jumps in a row, often around 4-6 strides apart
Single- an individual jump that's not a part of a line
Outside- a line or single that's ridden parallel to the longside of the fence
Diagonal- a line or single where you have to turn off the rail and ride from one corner to the corner diagonally from you.
So a lot of the beginner level hunter coarses (is it safe to assume you're going to be starting off at a beginner level?) are pretty simple and there shouldn't be too many jumps in there. In fact, in several of the arenas they often only have something like 2 outside lines, a diagonal line, and a diagonal single. Maybe another random single in there. A course would be something like, Outside line, diagonal line, diagonal single, outside line. I've even seen some that were, outside, outside, outside, outside! Yeah, basically they just went around and around on the rail! So when I look at the course diagram I repeat it to myself over and over again, outside, outside, diagonal, diagonal (or whatever the course is). Remember the first jump because here's a hint, let's just say that you go down an outside line. What other options do you have? They aren't going to make you do any tight or difficult turns. So either the other outside line or one of the diagonal lines. Does that make sense? Your options are limited! So stand there a while at the gate and just picture yourself going over every fence in the order that you're supposed to. Here's the hard part, you'll probably be doing a couple of courses! So once you finish one course, erase it from your mind completely! You'll definitely get the hang of it quick. And if you go off course? Oh well, it's happened to everyone at some point! Good luck!