From what I understand, you purchased your domain name from Google while signing up for GApps. You'll need to make some dns/Forwarding modifications. Log into the GoDaddy Domain Control Panel through the GApps Advanced DNS Settings (Dashboard: domain names -> DNS link).
Once logged into GoDaddy, click on your domain name. While on this first page, click on Forward:Enable forwarding. Pick 301 or 302. In the box type http://sites.google.com/a/mydomain.com/sitename/Home (use the same url you see when you clicked on Go to my home page. It might not show the Home, that's OK. Click on the Masking tab and Enable it. You don't need to put anything into the boxes. This will keep http://mydomain.com in the browser address box instead of the long sites.google.com... address.
Now click on the Total DNS Control and MX Records. Make these changes: remove the 3 A records that point to Google servers. These will typically have the following IP addresses in the record: 64.233.179.121, 66.249.81.121, and 72.14.207.121. add the following A record:@ pointing to 64.202.189.170 with a 1 hour TTL.
Change the CNAME for www. Point to @ instead of ghs.google.com. Back in the GApps control panel, you will need to click on Web pages in the Dashboard and under the custom url, check the default setting.
WAIT for up to 48 hours for the dns and Forwarding changes to propagate to necessary servers around the world.