Open Facebook and log in
Tap the menu icon
Go to Settings & privacy
Tap Settings
Tap Accounts Center
Tap Personal details
Tap Contact info
Select your email address
Tap Add email address
Enter the new email address
Tap Add
Confirm your password if prompted
Check your new email inbox for a confirmation message
Open the confirmation email
Tap the confirmation link
Return to Facebook
Set the new email as primary if needed
Remove the old email if desired