Open your web browser and download the Android Studio bundle from http://developer.android.com/sdk/index.html.

Run the downloaded DMG file. In the window that appears, drag the Android Studio icon into Applications and wait for Android Studio to be fully copied on the system.

Run Android Studio from Launchpad.

If an error Unable to find a valid JVM appears (because Android Studio cannot find a suitable JRE when launched), you can run Android Studio from the command line as follows (using the appropriate JDK path):

export STUDIO_JDK=/Library/Java/JavaVirtualMachines/jdk1.7.0_71.jdk
open /Applications/Android\ Studio.apps

If Android Studio proposes to import settings from a previous installation, select your preferred option and click on OK.

In the next Setup Wizard screen that appears, select the Standard installation type and continue the installation.

Complete the installation until the Android Studio welcome screen appears. Then, close Android Studio.

Go to http://developer.android.com/tools/sdk/ndk/index.html and download the Android NDK (not SDK!) archive suitable for your environment. Extract it inside the directory of your choice (for example, ~/Library/Android/ndk).

To easily access Android utilities from the command line, let's declare the Android SDK and NDK as environment variables. From now on, we will refer to these directories as $ANDROID_SDK and $ANDROID_NDK. Assuming you use the default Bash command-line shell, create or edit .profile (which is a hidden file!) in your home directory and append the following instructions (adapt paths according to your installation):

export ANDROID_SDK="~/Library/Android/sdk"
export ANDROID_NDK="~/Library/Android/ndk"
export PATH="${ANDROID_SDK}/tools:${ANDROID_SDK}/platform-tools:${ANDROID_NDK}:${PATH}"

Log out from your current session and log in again (or restart your computer). List the Android devices connected to your computer (even if none currently are) with adb to check whether Android SDK is working. No error should appear:

adb devices

Check the ndk-build version to ensure that NDK is working. If everything works, the Make version should appear:

ndk-build -version

Open a terminal and start the Android SDK manager with the following command:

android

In the opened window, click on New to select all the packages and then click on the Install packages... button. Accept the licenses in the popup that appears and start the installation of all Android packages by clicking on the Install button.

After a few long minutes, all packages are downloaded and a confirmation message indicating that the Android SDK manager has been updated appears.

Validate and close the manager.