To change your Facebook password, follow these steps: Log in to your Facebook account on a computer, click the down-arrow icon at the top-right corner of the screen and select 'Settings,' Click 'Security and Login' in the left column, click the 'Edit' icon next to 'Change password' in the right window, enter your current password and then enter the new password, retype the new password and click 'Save Changes' button to change password on Facebook.