How can I book a new court on the club kiosk screen?

Unlock the screen and tap the green Courts button. You'll be able to navigate to any day and select a court on the court grid displayed. Click on a court that is free (it will have a blue Book button). And  a window will popup asking you with whom you'd like to make the booking. If you don't have an opponent or match in mind then you can also elect to simply reserve the court for your own use - though there is a club limit on how many you can reserve like this at one time.