[Update April 2016] This answer is now outdated, custom naked domain mapping is supported, see Lawrence Mok's answer.
See http://www.google.com/support/a/bin/answer.py?hl=en&answer=91077 for the details. Once you have signed up for Google Apps for Your Domain:
# Sign in to the Google App Engine admin console.
# Go to Administration > Versions
# Click the 'Add Domain...' button under Domain Setup.
# Enter your domain name in the 'Domain Name:' field
# Click 'Add Domain'. You will be directed to the Google Apps administrator console to complete the process.
# Log in to the Google Apps control panel with your administrator account.
# Accept the terms and specify the access URL you'd like to provide for your application.
# Click 'Accept
You can't use a naked domain, though, such as whatever.com (but www.whatever.com does work), because:
Due to recent changes, Google App Engine no longer supports mapping your app to a naked domain. If your domain registrar supports URL redirects, you can redirect from http://yourdomain.com to your app, which can be served from domains like http://www.yourdomain.com or http://appid.yourdomain.com.
as specified at http://www.google.com/support/a/bin/answer.py?answer=91080
[Update April 2016] This answer is now outdated, custom naked domain mapping is supported, see Lawrence Mok's answer.
I have figured it out!
First off: it is impossible to link something like mydomain.com with your appspot app. This is considered a naked domain, which is not supported by Google App Engine (anymore). Strictly speaking, the answer to my question has to be "impossible". Read on...
All you can do is add subdomains pointing to your app, e.g myappid.mydomain.com. The key to get your top level domain linked to your app is to realize that www is a subdomain like any other!
myappid.mydomain.com is treated exactly the same as www.mydomain.com!
Here are the steps:
www and click Addwww for your domain and point to ghs.googlehosted.comNow you have www.mydomain.com linked to your app.
I wished this would have been more obvious in the documentation...Good luck!
[update 2015-09-28] Now Google lets you add custom domains (including naked domains) and setup SSL without the need of Google Apps. For details refer to here: https://cloud.google.com/appengine/docs/using-custom-domains-and-ssl?hl=en
I just discovered today (as of 2014-04-11) a new custom domain settings page is available from Google Developers Console:
1. Go to https://console.developers.google.com/project
2. Click on your project
3. On the left click "App Engine"
4. Click "Settings"
There you go! You can configure custom domain without the need of Google App account!