Q: How do I log out of the App Store because I. Got a new Apple ID and it keeps piping the old one up!!

Hello there, @jaidynschroeder123.

The following Knowledge Base article provides some great guidelines for accomplishing what you are looking to do:

iOS: Changing the signed-in iTunes Store Apple ID account

http://support.apple.com/kb/ht1311

Particularly:

Changing your Apple ID account

Tap Settings > iTunes & App Stores, then tap the Apple ID signed in.

 

Sign out of the current Apple ID account and then sign in with another account or create a new Apple ID.

Thanks for reaching out to Apple Support Communities.

Cheers,

Pedro.