When logged in to App.net click the drop-down arrow next to your username in the upper right corner.
Then go to Settings
-> Profile Click on 'Change' next to your email address.
You will need to your new email address twice, then enter your password to confirm.
Click ‘Change Email’ to save.
You will then be sent a confirmation link in an email to the new address you entered. You will need to click that link to confirm you email address change.