Firstly, I think you should take riding lessons with a trainer and ride school horses before you own your own horse. Through riding school horses you will get a feel of what kind of horse you like, and a trainer will help you develope the right skills and position to ride horses competativly.
Engilsh consits of Dressage, Show Jumping, Eventing, English Pleasure, Hunt Seat, and Hunter Jumpers/equitation.
DRESSAGE - Dressage is the basis of all riding. It started out as the training grounds for military horses. Dressge litteraly translates into - to train. In dressage you are working on getting the horses haunches under them, pushing forward so their head and neck come down and around and you have full control of the horse, but only after you have the proper tempo and rythem. You then work on getting the proper bend out of the horse, then collection and extention. All english riders should focus on dressage at least 3 times a week in their riding. It builds the foundation for a solid horse and rider. At the highest levels, horses go to the extremes of collection and extention. Riders also choreograph some routines to music. You also work on lateral movements suppling thehorse around your leg. In compeitiion you ride in a ring with letters on the outsides indicating where certian movements should be done. Judges score you on how well behaved your horse is, how well the movements are done, and how supple both rider and horse are. Highest scoring pair wins. Here is a video of dressage done properly.(I think, I havn't seen the video in a long time.)
SHOW JUMPING - Show jumping is where horse and rider go around a set course of jumps in an arena. The objective being to get the fastest time without knocking the poles down. every time a pole comes down or you go over the time, you get penilties. If there are multiple riders that go inside the set time with no knocked rails, you go into a jump-off. Fastest time wins. Show jumps can be straight up and down verticals to big spread jumps. Show jumping causes the horse to be brave and scoopy and to know where their feet should be placed. A rider needs to know their horse and how to get the best out of turns and the horse must be able to adjust from a quick gallopy canter to a light collected canter easily. At the highest level the jumps are usually around 5'6"
EVENTING - In eventing you do both dressage and show jumping, but in the middle you do Cross Country. As you already know what both dressage and show jumping is, I will explain cross country and how an eventing show works. Cross country is where you are out in open feilds and woods, jumping solid jumps and natural terrian at a gallop. You would jump up and down large banks, over logs, go through water, and have your horses bravery tested. You have to have a very well trained and brave horse to event competativly, along with a strong mind and body to go around a XC course for 7 minutes in galloping position. At a show you do dressage first, which determains your base score (which should be low because lowest score wins). Then you would either do XC or SJ. Out on the XC you get points added to your score for run outs, refusals, or going over your optimum time. If you fall, you are out of the compeition. The same rules apply for show jumping, only if you knock rails, you get penalized too. The lowest score of the weekend(events are usually held over 2 days for lower levels and 3 for the upper) wins. I myself event.
ENGLISH PLEASURE - Basically you want the horse to be relaxed and supple. The judge is looking for a horse that they would want to ride. The head and neck should stay level with the withers. HUNT SEAT AND HUNTER JUMPERS - In these classes the judge is looking for an easy going horse, with good form, that is easy to ride. They have a good stride, want to work, and the rider is not having to do much. The horse must be clean over jumps, and look nice.
EQUITATION - Probably one of the harder classes because it is the rider being judged. You must have the proper position and know how to support your horse. You must be a good rider with the "picture perfect" Jumping position on the horse.