Google is enforcing new apps infrastructure to every user starting from Jan 2011. If your account hasn't been transitioned to the new infrastructure, please do so by logging into your Google Apps admin account and follow the instructions on the top banner. After the transition, Google Apps email account will be working the same way as regular Gmail account. You just log in with full email address, including the domain name. Please contact Google Inc. if you had difficulty transitioning your account as it's beyond iMailG's support scope.
Since iMailG 7.0 we also added the legacy Google App mode. For Google Apps user whose account has not been transitioned to new Google infrastructure yet and some Enterprise user using a non-standard Gmail login page, please fill the corresponding settings field with the web URL that is used when you login on a computer browser. e.g. assuming your domain is abc.com, it could be either https://mail.google.com/a/abc.com or http://webmail.abc.com. Then go back to turn on the "Restart iMailG" option at the bottom.
Another common workaround is to create a personal Gmail account as proxy, by forwarding all your Google Apps emails to the proxy and also set the proxy account to send emails out as if they were from your Google Apps email address. Then use iMailG to access this proxy account instead. This way you can fully enjoy the offline feature of iMailG that lacks in the legacy mode.