If you cannot find the Google Play app shortcut on your phone, you can try a few things.
By default, the application should be installed and at least listed on the screen that displays all the apps.
One thing you can do is to do a factory reset for your phone, it’s not that bad, you also get rid of bloatware. It might take up to 30 minutes to reconfigure all back if you didn’t used that many apps.
If that won’t do it for you, you can install a backup .apk file that contains Google Play. Download from here, it has 9 megabytes.
Unzip the archive, copy it into your phone by using an USB cable and click on the file in order to install it.
The version is: com.android.vending-5.0.31-80300031-minAPI9.