It is quite easy to groom a cat for show and most of it is in the bath, but it does require lots of practice to get the cat looking wonderful. In Australia we are not allowed to sculpt our show cats, as they would be disqualified. This is allowed however in some other countries. We tip the ears and pluck around the face and also trim the hair around the eyes to enhance the roundness of the eye if necessary, but it should not be obvious and must still appear natural.
Buy a good quality shampoo, a degreaser; the sort that car mechanics use to get gunk off their hands and a good quality dishwashing liquid, make sure its not a lemon one. A wide tooth comb, a narrow tooth comb, a slicker brush, nail clippers, small scissors, eye cleaner, cotton swabs, mousse. Additionally you may require talc, chalk block, eye drops.
Start off by clipping the claws. This saves getting scratched inadvertently, plus saves the furniture. Hold the cat gently under one arm or on a table, press gently on the bottom of each toe to extract the claw and clip.
Tip the tufts from the ears, to make them appear more rounded to conform to the standard. This can either be done with scissors or your fingers.
Ensure that the coat is free of knots. Comb the coat through to make sure there are no tangles at all. If you give a cat a bath when it has knots they are very hard to remove afterwards. If there are any large knots use fingers to carefully and gently remove and if they are large use a quick-un-pick, the sort that dress makers use.
Check the ears to make sure they are clean.
Put a handful of degreaser in your hands and spread it all over the cat apart from its face. Put dishwasher over the top of that and gently rub it into the dry coat. Wash off thoroughly with a spray attachment, attached to your tap. When it is ALL off, use a good quality shampoo and rinse, do this twice, you may have to experiment with which shampoo to use as it depends on the coat texture and colour. When you have finished rinsing the coat out, rinse some more and more again. It's very important that you get all of the soap out of the coat.
When you have finished rinsing, pat the coat dry and get as much water as you can out of it, but do not rub. Put a small amount of mousse in your hand and pat into the coat, and then blow-dry. I prefer to dry the back end first, the tummy and then work my way forward to the head, but it doesn't really matter which order you do it in. The most important thing is to get them bone dry. Dry off one section before going on to the next using a wide toothed comb and gently lifting the coat up and forward as you go. When you have finished and are sure the cat is dry, keep on drying for at least another ten minutes for an adult cat. If you stop too soon the coat will still be slightly damp and this is what causes curls and waves so dry, dry and dry some more. Don't forget the legs, feet and behind the ears.
You probably will not need to use the degreaser every show and it often isn't necessary at all for kittens. Have a practice run before you show them but the main things are no shampoo & no dampness left in the coat. I normally bath my Persian cats the day before I show them and my Exotics three days before, sometimes if the coat is still looking good from the week before and you have been looking after it a bath is ok every two weeks.