How do I install Android Studio into IntelliJ?

Android support is bundled with IntelliJ IDEA (either Community Edition or Ultimate). All bundled plugins are activated by default. There isn't anything you can (or need to) install separately.

Now, because Android Studio is limited to Android projects built with Gradle and IntelliJ IDEA is more generic, there are certain differences in functionality between the two (Android Studio always builds projects with Gradle, while IntelliJ IDEA has its own build system capable of importing Gradle build files; the new project wizard in Android Studio is different). There is no possibility to modify IntelliJ IDEA Ultimate to match Android Studio in those aspects.

Android Studio is just an IDE with a custom compilation of IntelliJ plugins. You can install / activate any IntelliJ plugin in IntelliJ IDEA Ultimate (but not the other way around). If you want "Android Studio", just activate the Android Support plugin (File -> Settings -> Plugins).