Getting recognized by Google

Hi, I'm very new to building web sites. I've got a site up that I really like (thanks to lots of advice on this forum!). The site is getting traffic, but even after a few weeks, it doesn't show up on a Google search.
I've registered the site with Google and done their verification thing, but still nothing. What am I missing? The site is kind of pointless if no one can find it!

Thanks,

Chris