I can't add much more to what has been said already.
Key points for showjumping:
Try and be at about a 45 degree angle (in front of the jump) to begin with and try and judge when the horse is going to be stretched up with the front feet tucked in, if you take the shot as the horse is about to jump you will find that with reaction time/delay you should get it about right. This is a 'classic' type jumping shot:
Having said all that don't be afraid to try some side on or in profile with either the horse stretched out as in one of the links earlier or actually clearing the jump like this one:
Notice also the exposure nightmare on this shot, light grey horse, dark background and very bright/sunny day. :bang:
If you haven't got a telephoto or zoom lens you can still get good shots, this was taken with the 18-70mm kit lens, just be careful if are close to the jumps as horses can veer off at the last second:
If you haven't done this before try and get the light behind you so you can have a reasonably easier time exposing. also try with the light at 90 degrees to the subject as the shadows will pick out the muscle definition and veins like with this horse;
I don't know what camera you have but use single point or group dynamic for fosusing, don't use all the sensors for the reasons mentioned above and use AF-C (or equivalent) so the focusing tracks the horse. Use as fast a shutter speed as possible for jumping so you can really freeze the action.
I wouldn't entirely agree with Renee's point about focusing on the eye when shooting showjumping. Two reasons for this, with single point it will be difficult to maintain accurate focusing on such a small subject, I tend to concentrate on the area near the bottom of the neck just in front of the shoulder and saddle. The other reason is that is you are shooting on quite a wide aperture (and you may well be to get a fast shutter speed) your depth of field will begin at the eye, whereas if you focus on where I do the chances are that you will have the horses head and rider in focus.
If you are doing some portraits keep an eye out for the more unusal shots. This is one of my wifes favourite shots, if you want one similar stick a wide angle on and stand just out of reach of the horse, you'd be surprised how many stretch out like this to try and reach you.
I can feel a tutorial coming on....