Q: I purchased an IPad Mini for my mother-in-law using my Apple ID. I need to open an ID for her and take mine off the Mini. How would I do this?

You have a couple choices.  Restore the iPad to Factory condition and create the new Apple ID as part of the setup process. One of the Setup screens offers this option.  This will effectively erase everything on the iPad. Which assuming you don't have anythng you wish to keep would be the better choice.

Alternatively you can go to Appleid.apple.com and create the Apple ID there.  Then go into The Settings App on the iPad and sign out of your Apple ID from Messages, Facetime, iTunes and App Stores, iCloud and whatever other service you are signed in to with it. Then sign in with the new Apple ID to those services.

Note however that any Apps you may have purchased with your ID on that iPad  will be forever tied to your Apple ID, and require it to Update.

Best way

What to do before selling or giving away your iPhone, iPad, or iPod touch

http://support.apple.com/kb/HT5661http://support.apple.com/kb/HT5661

Apple ID: Changing your Apple ID

http://support.apple.com/kb/ht5621http://support.apple.com/kb/ht5621

Using your Apple ID for Apple services

http://support.apple.com/kb/HT4895http://support.apple.com/kb/HT4895

Apple ID: What to do after you change your Apple ID

http://support.apple.com/kb/HT5796?viewlocale=en_US&locale=en_UShttp://support.apple.com/kb/HT5796?viewlocale=en_US&locale=en_US

iTunes Store: Associating a device or computer to your Apple ID

http://support.apple.com/kb/ht4627http://support.apple.com/kb/ht4627

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

http://support.apple.com/kb/ht1311http://support.apple.com/kb/ht1311

How to Delete an Apple ID

http://www.wikihow.com/Delete-an-Apple-IDhttp://www.wikihow.com/Delete-an-Apple-ID

Apple ID Support - Manage Account

https://www.apple.com/support/appleid/manage/https://www.apple.com/support/appleid/manage/

Create an Apple ID

https://appleid.apple.com/cgi-bin/WebObjects/MyAppleId.woa/wa/createAppleIdForIK B?localang=en_US&path=https://appleid.apple.com/cgi-bin/WebObjects/MyAppleId.woa/wa/createAppleIdForIK B?localang=en_US&path=

 Cheers, Tom