If you want to install the Google Play Services on your Android device the easy way, then you only have to use your local app repository. The Play Store offers apps that are officially allowed to run on your Android smartphone or tablet.
All you need to do is to visit the Play Store and search for the Google Play Services on the search bar. You will have a list of suggested apps that correspond to the app you are searching. Simply tap the first one and you should be on your way to downloading and installing Google Play Services on your device.
However, there are instances when the Play Store gets into trouble and stops working properly. Therefore, you need an external source to download Google Play Services to run on your device. Take note that whatever the Play Store does with your apps goes via this Google service, so you need to download an APK version and install it on your device.
However, it is important to determine the version of Google Play Services you need to download for your device. Thus, you need to go to Settings > About Phone > Android Version. Once you determine the version, go to Settings > Security > Unknown Sources and tick the switch on.
A 3-number suffix should guide you when choosing the right version of Google Play Services APK to download. The 3-numbers are broken down as the following, namely the Android version, architecture of the CPU, and DPI or dots-per-inch. The current version of the Play Services can be found via Settings > Apps > All Tabs > Google Play Services.
Downloading just any version of Google Play Store APK should do more harm than good. It could even make the situation even worse if you install an incompatible version of the file onto your Android device.