Hello,
To sign out of your Dad's Apple ID completely, do this:
Settings -> iTunes & App Store -> Tap on the Apple ID email -> Sign Out -> Sign In to your Apple ID.
You might also want to remove his iCloud account and Messages as well as FaceTime in the settings.
If you need to create your own Apple ID (Without Credit Card), follow this tutorial: http://iosgods.com/topic/1725-tutorial-how-to-create-a-usnzca-apple-id-without-a-credit-card/
Also, the apps which are currently installed on your Device are from your Dad's Apple ID so if you want to update them, you will need to enter his password. To transfer them over to your Apple ID, you will need to reinstall all the apps while logged in with your Apple ID.