I've been given an Ipad, and I'd like to establish my own identity and remove the previous one. How do I switch ownership of the device?

You will need to turn off Activation Lock from within her online iCloud account.

https://support.apple.com/en-us/HT201441

ASC - Late 2012 Mac mini, macOS 10.15.4; Watch, series 5 GPS/cellular, watchOS 6.2; iPad Air 2, ipadOS 13.4; iPhone 8+, iOS 13.4; TV 4th Gen, tvOS 13.4;  HomePods, audioOS 13.4 and Airport Express w/ Airplay 2

Do you have access to another WiFi network where you can try? That has worked for several people.

Try a restart.

Restart your iPhone, iPad, or iPod touch         

Try a forced restart.

Reset Device.      

If necessary

Hard reset.        

Do a backup and try a factory reset. Then restore from your backup.

Restore to Factory setting.      

Backup - Restore your device from an iCloud or iTunes backup.      

You say "I have her ID and password, security questions and all that" If you have it all, then there should not be a problem. Is it possible that your are not remembering her password correctly? But, yet, you indicate that you know the answers to her security questions. Given that, have you accessed her Apple ID account to change her password? You should be able to so if you know the answers to her security questions. Is the phone showing activation lock as Dah•veed mentioned. If so, then there is no way we can help you to systematically recover the pertinent Apple ID password. I would contact Apple support using the options below, and see if they will remove the activation lock assuming the phone is activation locked.

Get a call from Apple support to help solve your problem using this link https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0245&symptom_id=23362

Apple ID Support https://support.apple.com/apple-id

Apple ID account security for country-specific and region-specific help https://support.apple.com/en-us/HT204169

Get Support: We’re here to help  https://getsupport.apple.com/. Go through the options to find the best support option.

See: What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support

then: Set up your iPhone, iPad, or iPod touch - Apple Support