How Long Until My Site Appears in Google?
Firstly lets just define the difference between a natural search and Sponsored Search.
Natural search is the process where search engines send a robot (also called a spider) to your site. A Robot is simply an automated program that catalogues content on your site and decides what your site is about. The search engine then places your site in the search results where it feels you best fit in. How popular your site is also plays a major part in where in the search results your site features. There is no charge to appear in Google's Natural Search.
Sponsored search is the process where you bid on a particular keyword/s. If you were selling Men's T-Shirts online. You might bid on the keyword "Men's T Shirts"... or even better something like "Men's Surf T-Shirts" (assuming you were in the surf industry).
The best way to get Google to locate / catalogue your site is to validate the site with Google and generate a Google XML Sitemap (your web developer can do this for you).
Also try and build up a few relevant links to your website (from other websites). As Google "crawls" through the web, it will find your site and catalogue it. Note good quality links to your website, is a sure-fire way of boosting your visibility in the search results.
It used to take up to 3 months to appear in Google's natural search, however with proper site validation, and some good links thru to your site - your site will appear alot quicker.