Changing your own email address
Your email address is part of your account settings. You can access your account settings via your user icon in the upper right, once you are signed in.
Press the Edit button next to the Contact Information heading, and enter your new email address. Your password will remain unchanged.
Changing someone else's email address (for administrators)
As an administrator, you may need to change someone's email address for them. Password resets are done via email, so if someone no longer has access to the email address on their account, and they also don't recall their password, it is better for you to change their email address for them than to have them create a brand new account. That is because they likely have links to participant profiles, squads, events, etc.
To access another person's account settings, bring up their details on the Security > Users page. From there, press the User Account Settings link.
You can then follow the same instructions as above for changing your own email address.