I used to use chalk and draw the course diagram in the barn aisle, and then have the students trot it on foot. We would practice where they entered the ring, started their hunter circle, where they'd ask for the canter, going deep in their corners, everything.
Doing this, along with drawing it on a dry erase board, are great tools. I used to keep a small dry erase board in my ring to draw exercises or courses on for students who really struggled with a spoken description.
People usually fall into one or a combination of learning styles: visual, auditory or kinesthetic. If you're an auditory learner, you can listern to your coach say "enter and track left, pick up your canter by the picket fence jump, then outside natural line, diagnol line, outside, diagnol." and go do your course. Very few people, IMO, are completely auditory learners. Drawing the course, or watching other riders ride the course, is good for visual learners, and actually walking the course, either for real or a chalk outline on a barn aisle, is good for kinesthetic learners.
Trying a combination of all the techniques is great when you're trying to learn a new skill, and it allow you to identify which technique works best for you.
Try to get your coach to put your number in late in the class so you can watch other riders ride the course. Separate yourself from your friends and family while you do this so you won't be distracted.
I also wanted to let you know you're in good company - this is a *very* common, almost universal worry among riders new to showing.
Good luck!
ETA: Hunter courses are usually posted the evening before or the morning of the show.