Add Google Play Services to Your Project in Android Studio

Step 1:-
Open the build.gradle file inside your application module directory.

Note: Android Studio projects contain a top-level build.gradle file and a build.gradle file for each module. Be sure to edit the file for your application module.

Step 2:-
Add a new build rule under dependencies for the latest version of play-services. For example:

apply plugin: 'com.android.application'
...

dependencies {
    compile 'com.android.support:appcompat-v7:21.0.3'
    compile 'com.google.android.gms:play-services:7.0.0'
}

Be sure you update this version number each time Google Play services is updated.

Note: If the number of method references in your app exceeds the 65K limit, your app may fail to compile. You may be able to mitigate this problem when compiling your app by specifying only the specific Google Play services APIs your app uses, instead of all of them.

Step 3:-
Save the changes and click Sync Project with Gradle Files.

Step 4:-
Open your app's manifest file and add the following tag as a child of the <application> element:

<meta-data android:name="com.google.android.gms.version"
           android:value="@integer/google_play_services_version" />

You can now begin developing features with the Google Play services APIs.