My daughter bought a new iPad and gave me her old iPad. However, her old iPad has her Apple ID associated with it.
I want to change that ID to the same Apple ID I use on my iPhone. Is that possible?
What part of the iPad do you want to add a new Apple ID to? There are several different places to enter an Apple ID.
Settings > Messages > Receive at:
Settings > Store > Apple ID:
Alternatively, you can go to the App Store, click on "Top Charts" at the bottom. Scroll to the bottom and you can sign out and enter a new Apple ID.
Go to Settings > iCloud > Account:
You don't say which Apple ID you want to change. The iTunes Store, iCloud and Messages all use Apple ID, and they can all be different. But yes, you can change, one, or all, according to your needs. Most of these changes are made in various Settings on the iPad.
Since there are two different Apple ID - you are in a situation where you can use both on one device but you cannot merge the two purchases and have only one account with the contents of both.
Hopefully, one account will be full of free purchases and you can just leave it behind. If not - try to make all future purchases on one account and only use the second account to load those past purchases you need.
This invokes signing in under the old account on each device. Downloading the apps and songs (authorizing that device for the "old" account). Then signing out and in to the new account for the rest of the songs and apps.
Just use care when asked to update apps - you'll need to remember both passwords when asked for each one needing an update.