Once a site is published, you should register your site with Google Webmaster Tools. Once your account is set up and your site is registered, within a few days you will receive a lot of feedback about the state of your website, both technical and from an SEO point of view.
After you have created your account you can start registering your site. First step in this process is always to prove that you are the owner of the site. This can be done in a number of ways, either by placing a small .html file in the root of your site or by placing a snippet in the head of your pages. It can even be done using your Google Analytics data.
You should always register your site using both the www and the non-www version, as 2 different sites.
Having registered the site, you can just leave it at that, but best is to add a little configuration.
If your site targets a specific region, select this region.
Secondly, you can specify a preferred domain, being either the www or the non-www version of your Joomla website. Make sure to specify the one that you have configured to be used, as earlier discussed.
Then finally, go to the Sitemap section and submit your sitemap.xml file, which is basically a matter of pointing Google to the location of your sitemap.xml file.
Bing and Yahoo webmastertools
Though being of much less importance, both Bing and Yahoo have a version of Webmastertools as well. Make sure to register your site there as well.