How do I change my old Apple ID on laptop to new one?

Below is some basic information on changing your Apple ID. But read the whole document linked below. And you will need to go to your Apple ID account (appleid.apple.com) for additional information. 

See Change your Apple ID https://support.apple.com/en-us/HT202667. 

See this basic information:

1.   Sign out of iCloud on all of your devices, including your iPhone, Mac, Apple TV, and PC. If you use the Apple Music app on an Android device or use the Apple TV app a smart TV, sign out of those apps.

2.   Go to appleid.apple.com and sign in.

3.   In the Account section, choose Edit.

4.   Choose Change Apple ID.

You can sign out of iCloud on one of your devices, or you can sign out on all your devices to stop using iCloud (for sign out purposes, see 1 above). Before you sign out of iCloud, make sure that you archive or make copies of the information that you store in iCloud. When you sign out of iCloud, you can't access or use the following services on your devices or your Mac.

And see What to do after you change your Apple ID or password https://support.apple.com/en-us/HT204071

If you are going to use a different ID on the laptop, the best thing to do is reset the computer so it 'belongs' to the new ID. That will help prevent future problems.

Selling old Mac