I accidentally changed my Apple ID and want to go back to the old one

What do you mean by 'changed my Apple id' ? If you updated the email address on your account then you can change it back via the same way e.g. tapping on it in Settings > iTunes & App Store on your iPad and logging into it, the Store > View Account menu option on your computer's iTunes, or http://appleid.apple.com

If you've logged into a different account then you can log out of if it on your iPad by tapping on it in Settings > iTunes & App Store, and on your computer's iTunes via the Store > Sign Out menu option.