Hello Jessica_apple_help,
We understand that you want to clear a MacBook Air from its prior owner so that you can use it. It is heavily recommended that you erase and set up the MacBook Air as new. The reason for this is that whenever an app is downloaded or an update, it links itself to the Apple ID that downloaded it. So even if you log into your Apple ID, everything downloaded prior under the former Apple ID will remain linked to the prior user. Additionally, it's important to have the device removed from their iCloud account. Details on what should be done prior to a new owner taking over the device can be found here:
What to do before you sell, give away, or trade in your Mac
You can manually save any documents and files that you want to preserve through those backup steps or just dragging them off onto a thumb drive or other portable device. Be sure that the prior owner has removed the Mac from their iCloud account with these steps as well: Remove a device in Find My on Mac Otherwise, there is the chance that the Mac could be locked as if lost or stolen and prevent you from using it.
Thanks for using Apple Support Communities!