
However, it's possible you may not need all three; Facebook allows you to add email addresses to your account without removing the old unless you want to.
Step 1: Add an Email Address
Login to your Facebook account, and click on Account, and then on Account Settings:






At this point, you can login using the new email address and your existing password. However, the old email address hasn't yet been removed, and will still get notifications.
That might be enough for you.
Steps 2 & 3: Remove the Old Address
Return to that email section, click on that change link again and you'll see something interesting:
Step 2: Select your new email address as the "Contact Email", and click on Change Contact Email. This will cause all subsequent notification to go to your new email address.
Step 3: After you've changed the Contact Email, a "Remove" link will appear next to the old email address. Click that if you want that email address completely disassociated from your Facebook account.