The website of the governing body of Horse Trials in the UK has all the information you need.
If you are a Pony Club member your branch Horse Trials trainer or your DC will help you work out where to begin. There are many rules, which are almost entirely for the safety of you, your horse, and spectators and helpers. Eventing is potentially dangerous, as are many other sports, and it is a sensible requirement that you prove you and your horse are safe competing around lower, less technical courses before you are allowed to move to bigger ones. Junior Open Novice (JON) and Junior Regional Novice (JRN) are not where you would start, you need to complete courses at BE90 (Intro) and then BE100 (Pre-Novice) before attempting Novice courses, which ask far more questions, and not only in terms of height.
You can buy a Day Ticket rather than becoming a member straight away. Your horse will also need a Day Ticket if it is not registered with British Eventing. The full entry fee still has to be paid, whether you have annual membership or a Day Ticket. Your first year's membership is eligible for a discount if you are a paid-up member of Pony Club or an affiliated Riding Club.
It's expensive - you are looking at up to around £100 in fees for a day of competition, and if you are eliminated in the dressage or show jumping you cannot go on to ride in the next phase. You need to be pretty sure of your competence and your horse needs to be fit and obedient.
The British Eventing office staff are extremely helpful and anything you can't find on the website can be answered with a quick phone call.