The Pokemon Go game is a free game for mobile devices and was launched in 2016 July, but only in USA, Australia and New Zealand and cannot be downloaded yet from other countries.
Pokemon Go was created by the Pokemon company (which is 75% owned by Nintendo) and Niantic which was founded in 2010 by John Hanke as Niantic Labs, an internal startup at Google.
So if you cannot find the Pokemon Go in Google Play Store then it means that it is not available yet in your country. But you can download and install Pokemon Go for Android from this link APKMirror.
Then copy the APK file to your Android device and launch the APK file with the File Manager and install the Pokemon Go game.
If you are looking how to install PokeMon GO for iOS then go here