In Google play click on the Settings tab and go to MyApps. There you will find whichever apps you've paid for or have downloaded accordingly.
If an app is requesting an update, you will find a list of apps waiting to be updated.
Now, there are two way to update these apps, manually or automatically. If you check on your smartphone settings (look for the icon that looks like a rounded mechanical circle) and then go to apps, every app that has a checkmark has the potential to automatically update itself. Else you will have to manually update them all on the first described step.
