Welcome to Android Central! I moved this from the Android Apps forum to General Help.
Does this happen on both wi-fi and mobile data?
Try going to
Settings>Apps>All, select Google Play Store, and Clear Cache/Clear Data, then Force Stop. Do the same for Download Manager. Now try again.
If that doesn't work, try going to
Settings>Accounts-Google, select your Google account, and remove it completely from the phone. Then add it back again, and see if that helps.
When you have a chance, head over to the Intros forum and tell us something about yourself!
Introductions - Android Forums at AndroidCentral.com