You can select to play just this game or you can do it as part of the Game Show. The former is quicker, obviously.
It'll be random on who goes first and you can skip the computer's turn by pressing A a couple of times. When it's your turn, hold the RS down and then flick it to the up position, straight down the middle. It will then show you what you've got. You'll get 2 more tries so keep the best and select the ones you don't want to keep with X to try and improve your 'hand' (you can press Y, I think, to show you a running order of best to worst).
Bowl your next two bowls and hopefully your 'hand' will end up being better than the computer's. If not, rinse and repeat. It's the best of 3 so you'll have to replay if you don't win either round.