How do I close background apps on the new iPad?

By design, it should not be necessary to manually close any open Apps. iOS/iPadOS should transparently and seamlessly manage its available resources as you switch between Apps and tasks.  Should you need to force-close individual Apps, you can do so from the App Switcher page...

To expose the App Switcher page, swipe-upwards from the bottom edge to the centre of the screen, pausing briefly before lifting your finger from the screen; you will see a thumbnail image for each of your currently open Apps. Apps can be force-closed by swiping the corresponding thumbnail off the top of the screen.