Uninstall previous updates
Generally, when you have a problem with an app you can just uninstall it and then reinstall it. Well that works for some apps, but the Google Play Store is a system app on your Android device. What you can do instead is uninstall previous updates to the app and this might help your problem.
You first need to head into your Settings, tap either Apps or Application manager, and you should either see all of your apps or you might have to choose All. From there find the Google Play Store and tap Uninstall updates.
If your Google Play Store is still not working then you need to go back and reinstall the updates. From there head down to our last solution.
Perform a factory data reset on your smartphone
If you're still facing problems after having tried all of the above, then you may have little choice but to do a factory reset. This is a drastic measure and there are consequences. All of your data will be lost. So you should perform a complete backup beforehand.
Once your data is backed it's time to do a reset. Go to your Settings and tap Backup & reset. Now, make sure the Back up my data slider is on. Tap Back up account to select which account you want your data backed up to. Ensure you have access to this account.
Once you've done this, go to the Backup & reset menu and tap the Factory data reset button at the bottom. Confirm that you want to do this, and your phone will be as it was when you bought it. Your data will be restored when you log back into your Google account.
Did these solutions work for you? Do you have any other advice to get the Google Play Store working again? Let us know in the comments.