The first think you need to do is log into your Facebook account.

Once logged into facebook.com, click on the “Settings” option that is at the
top toolbar in blue.

On the Settings page, the third option on the list will be “Email.” Click on
the “change” link on the right hand side of the screen.

Once you click on “change,” you will see a new field appear called “New
Email.” Simply enter your new email address in the “New Email” field and
click “Add New Email.”