I would recommend turning off data when you're not using the phone to reduce your usage, here are two other tips...
Update Over WiFi
You can set your phone to only update apps over WiFi which will reduce your data usage. Here is how to change the Play Store settings for how apps are updated:
1. Open the Play Store.
2. In the top left corner tap the menu icon.
3. Tap Settings.
4. Tap Auto Update Apps.
5. Tap the option you want. The WiFi option will only use WiFi. "Update apps anytime" can use your mobile data. "Do not auto update apps" will not update any apps.
Background Data
Some apps use background data, which means they use data when you're not using the app like zuben mentioned with Facebook. You can disable background data on an app by app basis so they wont use your mobile data when you're not using them. Some phones might not have this option though.
1. Go to your phones Settings menu.
2. Tap Data Usage
3. Scroll down to the app and tap it.
4. Scroll down and tap to check Restrict Background Data.
For some apps you wont get some updates/notifications after after doing this when you're not using that app. Also I believe that only shows apps that have already used data so with a brand new phone there might not be many apps listed yet.
Or you can disable all background data > Settings > Data Usage > Menu > Restrict Background Data. If Restrict Background Data is turned on here you wont have the option to disable it for each app as described above. There is also an option to turn off Auto Sync Data.