Once you have logged into Moodle you should select the Profile option under your profile image in the top right hand corner of the screen:
Click on the Edit Profile link on the next page.
You can change your email address here and then save these changes by selecting Update Profile at the bottom of the screen.
You will now receive messages from your lecturers and fellow students to this new email account via Moodle. If you need to reset your password for the Moodle site at any stage the automated email with your new password will be sent to this email also.