There are two ways to request a Developer Account.
Using a Web form
Visit http://developers.mailup.com/setupen to request a developer account (or http://developers.mailup.com/setup if you prefer for the Italian version for both request page and developer account console).
From within a MailUp admin console
Select "Build your own MailUp application" on the bottom of Settings > Account settings > Developer's corner > Integrations web page