If you want your site to show up in Google search results you basically have to pimp your site everywhere. Find list sites with similar interests, put your Web site in your signature on forums, take out paid advertising. Basically anything you can do to get your site out there. Google ranks things higher based on how many links there are to a site, thus the google-bombing phenomenon. Also, sometimes it is really hard to break into the google ranks on certain subjects. For example my professional Web site and my Web comic show up near the top of the list for their respective titles, but when you try to google my name you have to click through a few pages because there was a soldier who died in Iraq with the same name as me who has tons of sites devoted to him.
As for Googling a specific phrase, just because your site says something unique does not mean your site will show up if you google that phrase even though you have been indexed. Exactly what is indexed by the googlebots is anyone's guess. They pride themselves on keeping that information secret (for good reasons too or the corporations would skew all search results).