My daughter gave me her iPhone 4 ...
To make it Truly Yours... Set it up as a New Device...
See Erase your device Here > http://support.apple.com/kb/HT4137
Go to Settings > General > Reset > Erase all content and settings
Also... See the wjosten post here...
Also see here...
Set Up as New Device
Go to Settings - iTunes&Appstores - tap her Apple ID - log out - log in with your own.
Please note that apps that have already been downloaded using her Apple ID need to be updated from time to time, and you'll have to log in with her Apple ID for that.
You can also just remove all those apps and download them using your own Apple ID to prevent that issue
I'd actually recommend fully restoring the device to factory settings using http://support.apple.com/kb/ht1414 so you can start fresh
but it's still your choice.
Hope this helps