How can I set up my domain name on Google App Engine?

I've made a website to go on App Engine, and have deployed it. I've redirected my domain name to ghs.google.com, and it successfully goes to my site.

The problem is that in the address bar, 'www.mysite.com' turns into 'myappid.appspot.com', and I haven't got a clue as to how I make it stay with 'www.mysite.com'.

It seems like such a simple thing, but It's starting to drive me insane!

How do I fix this?

How do I add my own domain to Google App Engine?

In the Google Cloud console, go to the Custom Domains tab of the App Engine Settings page. Click Add a custom domain. If your domain is already verified, the domain appears in the Select the domain you want to use section. Select the domain from the drop-down menu and click Continue.

Have a look at this quick guide, in essence:

Add a CNAME for www.yourdomain.com and point it to ghs.googlehosted.com.

Sign in to your application via appspot.com.

Click the Administration → Application Settings link.

Click the Add Domain... button under the Domain Setup section

Add www.yourdomain.com in the domain name box and click the Add Domain... button

With respect to the naked domain question. Please take a look at: http://code.google.com/appengine/kb/general.html#naked_domain and follow the link provided there.