How do you get your website...

so it comes up during a Google search?

[snowman]

Do you have to e-mail someone at Google so they'll include it in their database or something?

[jdMorgan]

snowman,

All you need is one incoming link to your site from a page that is already in Google's index, and Googlebot will come find you. Of course, the more incoming links the better. Incoming links from the ODP and from Yahoo! are very good.

Brett's Successful Site in 12 Months with Google Alone [webmasterworld.com] tutorial may be helpful, and a search here on WebmasterWorld for "new site" may also prove interesting.

HTH,
Jim