Go to Settings > Apple ID, iTunes, iCloud and App Store
Tap your Apple ID
Sign back in with the correct ID
Please note: If you fully changed your Apple ID, all apps downloaded on the previous ID are tied to that ID forever. When they need to be updated, you will HAVE to enter the Apple ID password they were downloaded under, so make sure you keep that password handy. Or you can delete those apps and repurchase them under your new ID. If all you did was change your Apple ID Password, this won't apply.