About two months ago, the home button finally gave out on the iPad my son uses. We're not thrilled about the idea of spending any money on a device doomed to replacement shortly anyhow, so we found some alternative ways "to press the home button" a.k.a. to return to the Home Screen.
Note: You will need to use the power button at the top of the iPad to turn on the screen when the device is asleep instead of the once-working home button.
Use iPad "Multitasking Gestures"
In the Settings app, under the General section there is a switch to enable Multitasking Gestures. One of the multitasking gestures is a four-finger "pinch" to go to the home screen. With this enabled, you can touch with four fingers, bringing your fingers close together in a pinching motion (like you pinch to zoom with two fingers when looking at webpages or photos) to return to the home screen.
Use "Assistive Touch"
Back in July, we wrote an article about using Assistive Touch to control your iPhone volume if the volume buttons break. Assistive touch will also provide a home button "button" on your iPad screen to press. We don't like Assistive Touch as much as the Multitasking Gestures for the broken iPad button, because Assistive Touch adds a button ever-present on the iPad screen which might get annoying.
You can read more about Assistive Touch on Apple's website as well. Obviously, the triple-click Assistive Touch toggle option is not as useful when your home button isn't working! ;)