If you search for your site in Google and it is not listed, then go through this check list:
Make sure it is actually not indexed. Do a Google search for site:http://www.yourdomain.com (for eg)
If that shows there are no pages listed, then work through this:
Make sure you are not using the noindex tag (common reason for WordPress sites)
Check your robots.txt file to make sure you are not blocking the Google crawler.
Check the logs to see if Google has crawled the site; if not check that there is nothing the web host is doing to block the Google crawler.
If the site is new, give it up to several months; make sure you have submitted a Google sitemap and use the ‘fetch as Googlebot’ function in the Google Webmaster tools.
Check in your Google Webmaster Tools account that there was not a request to remove the site.
If it is a new site, then what was on the site before you owned it? Could it have been banned from Google for activities that are contrary to the Google Webmaster Guidelines?
Google also tends not to index sites that have no backlinks to them from other sites, so make sure you have some links to the site (it is via the links that the Google crawler finds the site; and also probably makes an assumption that a site with no links is not that important).
Is most of the content on the site copied from other sites? If so, then Google may not want to index your site as it offers no value to the web.
If none of those reasons apply, then there is a high probably that Google has taken manual action against the site. After fixing up the site; complying with the Google guidelines; then submit a reconsideration request.