When creating one Intent so that MyActivity reacts to a User pressing the Home-button is easy using the XML markup:
<action android:name="android.intent.action.MAIN" />
<category android:name="android.intent.category.LAUNCHER" />
<category android:name="android.intent.category.HOME" />
<category android:name="android.intent.category.DEFAULT" />
You can't permanently override the Home button without the user confirming it.
One argument for why this is the case is a security one. The Home button is the one way a user can be guaranteed to exit any application. If you could make the Home button launch your application instead of the Home screen without the user confirming this change, it would then be very easy to write a malicious application that hijacked a user's phone.
Alternatively, your application could contain a replicate Home Screen that harvested a user's Google account details; not that hard since the source is available. If your application could silently replace the default Home Screen, it would be hard for the user to tell this had happened.
Also, do you really want to override Home? Home is like an emergency escape button. Pressing Home twice will always take a user back to the center panel of the Home Screen, so whatever application they're running, it's easy for a user to get back to somewhere they know. You shouldn't really be overriding this unless you're producing a full Home replacement.