Disassociate an Apple ID from a computer

Solution 1:

Go to System Preferences, and check "iCloud" and "Internet Accounts". Sign out where necessary, and once neither of them list your personal account, you're good to go.

You may also want to make sure your web browsers don't remember any of your passwords.

Solution 2:

Removing an associated device or computer from an Apple ID

To remove a device or computer from your Apple ID:

1. Open iTunes.
2. Sign in to your Apple ID by choosing Store > Sign In from the iTunes menu.
3. Choose Store > View My Account from the iTunes menu.
4. From the Account Information screen, click Manage Devices.
5. Click the Remove button next to the device name you would like to unassociate.

Note: Removing a device from your Apple ID does not override the 90-day timer. You must wait 90 days from the day the device was first associated with your Apple ID before it can be associated with another Apple ID.

Source: iTunes Store: Associating a device or computer to your Apple ID