It can take a little while for Google to initially find your site and index, and longer for it to start ranking by specific keywords. It looks like your site has been live about a month, and Google has already gotten a few of the pages:
If you give it a little longer Google should get the rest of the pages of your site. If you want to work on your ranking, I recommend taking a look at our Ultimate Guide to SEO.
So, when you say, "a little while for Google to initially find your site," can you give me an estimate on that?
Several days? A couple of weeks? More? (Please say no to this...)
A lot of factors go into search rankings. Domain name, age of site, content, visitors, seo settings, etc. It's not possible to give a time frame for what you are looking for, unfortunately. However, you should definitely check out the link Adam posted. Even though you don't have control over Google's process you can still do everything in your power to make sure your site has all the needed seo tweaks.
Google needs time to crawl all your URL. You should wait for at least 1-2 month to see your pages on Google search.