The only reason Google ever lists a website in their search results is when other websites link to it, therefore giving it a "vote of popularity", or if you submitted it to them manually. If you have done these things, it will take some time to resolve it but here's a few things you can do to speed things up:
So the way to get your IconoSites address (i.e. yoursite.iconosites.com) replaced with your custom domain address (i.e. www.yoursite.com) from Google is to remove any links pointing to your IconoSites site address (from your facebook, twitter account or anywhere for example), and change them to your custom address. You will want to make sure NO links are pointing to your site using the Iconosites site address.
Then, you also will want to build more links to your site using your custom address. For example, add links to your website (using your custom domain, of course) on your Facebook, Twitter, Linked in accounts and ask your friends to add your link to their blogs or anywhere else you can find. Soon enough, google will see that this is the address that you prefer, and their software will automatically update the results. This could take anywhere from 4-6 weeks....if you build links quickly, it can happen in a matter of days.
It is important to understand that Google is it's own company and they decide exactly which websites to include in their search results. This has absolutely nothing to do with IconoSites. If you want to learn more about Google and their search results, we recommend reading some articles on the internet. If you want to learn about how to improve your search rankings, be sure to check out our 3-part series on How to SEO your Website.