My granddaughter has been using my old phone. I have started a family sharing thing and got her own Apple ID so how can I change an Apple ID without resetting the phone?

Sign out of your iCloud services and your account on your old iPhone - the one your granddaughter has - then sign in with her iCloud account. If I understand your post, she has already accepted membership of your group. If not this is the time to do it, once her email has downloaded.

The phone does not need to be reset, at least not at this stage. Because she is a part of your group she can share your purchases such as the games and the other apps. As I recall, this is on by default, but it's been ages since I set up a family group so I can't be sure. Just check that purchase sharing is on; you can do this by following the steps in How to share apps and purchases with your family:

Turn on purchase sharing using your iPhone or iPad

1. If you haven't set up Family Sharing yet, set up Family Sharing.
2. Open the Settings app.
3. Tap Family. If you don't see Family, tap your name, then tap Family Sharing.
4. Tap Purchase Sharing.
5. Tap Continue and follow the onscreen instructions.
6. To confirm which payment method will be billed, tap Purchase Sharing again and check the Shared Payment Method information. This will be the family organizer's default payment method.

Once she has backed up the phone to iCloud the data will be on iCloud in order to restore it should you need to reset it in the future, but there shouldn't be a need for this.

But before all of this make sure you have a backup of your phone as it is currently.

A few things to note:

If you have been sharing an ID and do not erase the device, your information may still be on the device. Do you want her to continue to have all that? I have never signed out of a device but I believe when you do so it asks if you wish to erase information in different categories. You may wish to investigate that and delete it for some if it just has your data.

Some things may be lost when a new ID is used on the phone. Some games, I believe, store score information as part of the ID that is using the game, so if she starts playing under a different ID she starts over again.

I also don't know that even if you have Family Sharing set up if the apps which were downloaded with your ID will update under her ID, or if she will have to delete them and then redownload them under her ID linked to your through Family Sharing.