"Open" is open to everyone, but it is usually trainer dominated. This would be the toughest level.
"Amateur" is for people who do not coach, train or ride for money. Sometimes you need proof of status, or to sign something saying that you haven't taken reimbursement for services like riding, coaching or training.
"Novice" is for beginners and will be the easiest. Usually there are rules as to the maximum number of first places you can have won to compete in these classes, but the rule can vary slightly.
Amateurs and Novices can show in Open, Novices can show in Amateur, but a Professional cannot show as an Amateur or a Novice. Some Amateurs can show in Novice, but usually cannot cross enter.
Good luck at your shows!