Short answer: You need to create Unity Android plugin of Android project using Google Cloud Messaging.
Details of how to create Android Unity plugin you can find Unity's official site.
Here are some details:
A) You have to start with google Android sample app, understand the push-related API methods
https://developers.google.com/cloud-messaging/android/start
B)You will need API KEY, SECRET
and ANDROID SENDER ID: Project Number assigned when setting up Google Cloud Messaging.
C) Your AndroidManifest.xml. Google Cloud Messaging has some minimum API level requirements for development and testing. Set minSdkVersion property appropriately.
D) Add the following new permissions after the existing element, replacing your_package_namewith the name of the app package for your project. To check the current name of your package go to File > Build Settings > Player Settings and select the Android tab. You will find it in the Bundle Identifier field.
<permission android:name="**your_package_name**.permission.C2D_MESSAGE" android:protectionLevel="signature" />
<uses-permission android:name="**your_package_name**.permission.C2D_MESSAGE" />
<uses-permission android:name="com.google.android.c2dm.permission.RECEIVE" />
<uses-permission android:name="android.permission.GET_ACCOUNTS" />
<uses-permission android:name="android.permission.WAKE_LOCK" />
E) Add the following code after the main activity inside your application tag, replacing it with the name of the app package for your project:
<activity android:name="com.gamedonia.pushnotifications.GamedoniaPushHandlerActivity" />
<receiver android:name="com.gamedonia.pushnotifications.PushBroadcastReceiver" android:permission="com.google.android.c2dm.permission.SEND">
<intent-filter>
<action android:name="com.google.android.c2dm.intent.RECEIVE" />
<action android:name="com.google.android.c2dm.intent.REGISTRATION" />
<category android:name="**your_package_name**" />
</intent-filter>
</receiver>
F) Use your unity functions to call methods written in your Android project, You can send push notifications from a server scripts.