How do I return to rotation mode?

Open Control Center on your iPad (more recent iPad's have you swipe from the upper right hand corner down) and find the icon with a lock in it. If it is red, rotation is locked. Tap it to unlock rotation. But also note that not all apps can be rotated on iPad and if it's a 3rd party app, which won't rotate, you need to contact the app developer as it's up to them to code rotation into their app.