There are as many techniques to grooming for a show, as there are breeders. Much depends on the age of the cat, the sex, time of year, color, and coat texture. Sometimes, daily brushing can cause more damage to a show coat than good. Check the coat several times daily, just by petting the cat, and if you feel the start of a small snarl, then comb it out using a wide-tooth metal comb. Never use a slicker brush for any type of daily, deep combing. The wire teeth of the slicker brush will tear out all the undercoat and leave only the hard, long guard hairs from the outer coat. This will leave the coat feeling harsh and wirey.
Most show Persian owners, bathe the cat at least the night before the show, though some can be done even a day or two before the show. Some people even bathe the morning of the show, both days. The most important part of the bath is the rinse. Be sure to rinse all the soap out. The biggest mistake many people make in grooming is leaving some soap in the coat. After the bath, push as much water off the coat in the sink as you can. Next put the cat on a pile of absorbant towels. Then using good quality, paper towels, soak up as much water as you can from all over the cat. Pay special attention to the face, head, front and back legs, belly, and tail. These are the hardest parts to get dry and the areas the cat is most likly to object to grooming. They are also the first areas to get crumpled and greasy. After the coat is almost dry to the touch, use a regular bath towel to "fluff dry" the cat. This will separate the coat and make it easier for air to get in and make the coat fluffy.
Powder is a very important grooming tool. It can help you in the drying proccess and in the show hall, help absorb grease as the day wears on. There is a process called powder packing: you can sprinkle small amounts of cornstarch baby powder into the damp coat, behind the ears, into the legs, and belly after bathing (then blow it out with the hair dryer). This will make a mess when you turn the dryer on...so you may want to practice this with dry coat first until you are comfortable working with powder.
If you are serious about showing, then invest in a professional grooming dryer, such as the Oster brand table top/cage dryer. Dryers run about $160 and should last forever. They are more powerful and do not get as hot as a regular "people" hair dryer. They also make a lower pitch sound, which does not seem to bother the cats as much. Best of all, it leaves both of your hands free to groom the cat while he/she is being dried.
Turn on the dryer. There are a couple ways to start. One way is to put the cat in a carrier. Turn the dryer on into the carrier and fluff the coat with your fingers every few minutes. If you do this, be very careful that the dryer does not get too hot (especially if you are using a regular "people" hair dryer). Another way is to put the cat on dry towels or a rack. Just set the dryer, cat, and all your grooming tools up on a table, and get comfortable. Start off by just having the dryer do the work, while you fluff the coat all over with your fingers. As the coat dries, you can start using either a wide-tooth metal comb or a pin brush (without any balls on the end of the pins). Do not use a fine-tooth comb, slicker brush, or any type of plastic brush. This will only make static or pull the hair out. From start to finish, a well-coated Persian (depending on size/age) will take anywhere from 2 to 4 hours to groom. The secret to growing a beautiful show coat is a bath and grooming every single week.