How to delete an event if the edit button does not appear

I assume that you are talking about the calendar app. When you tap on the event are you not getting a window that pops up with the Edit button at the top ? Have you tried quitting the app completely and restart the iPad?

Go to the home screen first by tapping the home button. Quit/close open apps by double tapping the home button and the task bar will appear with all of you recent/open apps displayed at the bottom. Tap and hold down on any app icon until it begins to wiggle. Tap the minus ➖ sign in the upper left corner to close the apps. Restart the iPad. Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.