Android Studio Installation and Setup

Prerequisites

unzip the Android Studio Bundle
launch Android Studio. This may take quite some time as additional downloads and setup steps are completed. These steps are necessary for Studio to run properly.
after the previous step is complete, it is necessary install the SDK and build tools. SDK Manager is located in: Tools --> Android --> SDK Manager. It is also possible to access the SDK Manager without opening a project by selecting it from the dialog box Android Studio presents at startup:

The SDK Manager window looks like this:

Make sure to install the platforms and tools that your project requires.

cpp-tests is a project you can run to get familiar with how to code using Cocos2d-x. To run this project with Android Studio:

import the cpp-tests project from cocos2d-x root/tests/cpp-tests/proj.android in Android Studio. Android Studio will do everything required. You can run cpp-tests by clicking on the Play button.

note: Android Studio is going to download many components. It may even throw errors that you just click to fix. These errors may include: gradle version updates, installing missing build tools, agreeing to license agreements, etc.

Starting a new project requires a few steps:

first, use cocos new ... to create your project. See the Cocos Command-line tool for additional help.
next, launch Android Studio.
next, you must specify what version of the Android SDK you are using. You can do this by modifying gradle.properties

Starting with cocos2d-x v3.15, you can use Android Studio 2.3+ to debug c++ code by setting breakpoints where you wish.

There are a few required steps to build in release mode:

change Build Variant to release
set signing information in gradle.properties
for lua projects, if you want to encrypt lua codes, you should set encrypt information in gradle.properties too

use the built in SDK Manager to install the SDK versions and build tools that you are targetting.

Note: It is important to note that Android Studio uses a location to install SDK versions and build tools that is not the same as if you were doing command-line development. Double check that you have everything you need installed from inside Android Studio.

Please see this F.A.Q for troubleshooting help.