How do I make an embedded Android OS with just one app?

By the sound of your question you want to create your own custom Android OS build. That is going to be more involved than developing ordinary Android apps and consequently you're going to have to do a lot of reading, especially the Android OS source code.

I recommend you start here at the Android Open Source Project.

Essentially you're trying to have a custom build of the AOSP where the "Home" is your application. If you look into /packages/apps/Launcher2 you'll find the code for the default Home screen.

If you look at the AndroidManifest.xml file in there, you'll see something like this:

     <activity
        android:name="com.android.launcher2.Launcher"
        android:launchMode="singleTask"
        android:clearTaskOnLaunch="true"
        android:stateNotNeeded="true"
        android:theme="@style/Theme"
        android:screenOrientation="nosensor"
        android:windowSoftInputMode="stateUnspecified|adjustPan">
        <intent-filter>
            <action android:name="android.intent.action.MAIN" />
            <category android:name="android.intent.category.HOME" />
            <category android:name="android.intent.category.DEFAULT" />
            <category android:name="android.intent.category.MONKEY"/>
        </intent-filter>
    </activity>

Essentialy, this says that this Activity reacts to the

android.intent.category.HOME intent.

When the system finishes booting (the ActivityManager more specifically), sends that intent. So, if you want your app to start instead of the Launcher, just create yourself an app with a similar intent filter and remove the default Launcher2 (take it out of the list in build/target/product/generic.mk and put yours instead). Also make sure the relevant .mk file has something like this:

LOCAL_OVERRIDES_PACKAGES := Home

So long as your app doesn't provide a way for the user to launch other apps using icons (like the Launcher does), no other app will be started; unless of course something sends an Activity-starting intent from some other path than the one controlled by your app - say by using the "am" command on the target's Android shell.