You know that you can swipe up and down in the window on the left where you should see Reminders. Are you sure that you haven't swiped up all the way? Did you go to Settings>iCloud>Reminders>On?
You can always try closing the reminders app and reboot the iPad and see if that returns things to normal operation.
Tap the home button once. Then tap the home button twice and the recents tray will appear at the bottom of the screen. Tap and hold down on any app icon until it begins to wiggle. Tap the minus sign in the upper left corner of the reminders icon. Tap the home button.
Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.