Only purebred cats aged 7 months or older can be entered in shows. Enter your cats in shows by clicking on the "Shows" link in the menu. To enter a show, search for shows that were set up for your cat's title (Novice for untitled cats), and click on a show name to view the cats that can be entered in the show. If you are a Star player, you will see checkboxes next to the shows and cats (it's pretty much self-explanatory).
When the show is run, the cat's traits will be compared to the standard by a script (it's not the show host who chooses the winners). The more a cat conforms to the standard for its breed, the higher it will place. Rufusing and ghostmarkings are generally not desirable (exceptions exist for a few breeds and colors), and will lead to point deduction if the cat has those. Cats that are sick, hungry, or in bad condition have less chance to win a show, so make sure your cat is well fed and healthy before entering a show! An aggressive cat will bite the judge, and a shy cat will try to run away, both of which also leads to point deduction. Each time a cat is one of the first five winners in a show, it will win a certain amount of showpoints (sp). If it has earned enough showpoints, it will get a champion title. The more points the cat has, the higher the title. Check the FAQ for details about the showpoints needed for each title.
As a winning cat's owner, you also benefit -- you will receive Tokens if your cat wins one of the first five places. The owner of the cat that gets first place will also receive the prize money.
Showing has no effect on a cat's stats, its genes or the number of kittens.