Yes, Google is big but you can get your site listed in 24 to 48 hours. Go to Google and look at "Submit a Site". STOP! That is exactly what everyone does and it takes months to get listed that way.
Now you if want to wait for your new website to appear in Google, stop reading this.
Here's the trick. Get a high Page Rank site to link to you. A PR (page rank) of 5 or higher will do the trick. Yes, it is that simple.
This won't guarantee you the #1 slot for all your keywords but it's a great start. At least you can be found. Google currently takes 6 to 9 months for a new site to appear - not even rank - but appear.
If you can find more than one PR5 or higher to link to you that just helps you even more.
As an example, go to Google and type in the search box, Parker Computer Guy. At this writing the site was appearing as listing #4. (Actually listings #2 and #3 are the Parker Computer Guy blog, www.parkercomputerguy.blogspot.com).
This is a brand new site! It can be found in Google and is listing #4.
This is simple, this is free. You can find plenty of sites to link to you. Search for sites that are in the same category as yours or use a link directory. There are several free ones out there, linkmarket.net and linkmetro.com for example.