Most websites don't show up in Google--- at least not on the first pages where you and everyone looks -- unless you take steps to make your site show up there. This is called SEO (search engine optimization) and this is a complex and time consuming process when done right. If you are in a competitive niche, like selling diet products or fishing equipment, you may never see page one. Of course if you are selling house sized asteroids or a similarly rare product, your page will be first up as there is no competition. Everything else falls between these two extremes.
There are basically two parts to website optimization---on page and off page. Both are important. The on page is usually pretty simple and straight forward and not overly time consuming. The off page is hugely important and involves massive amounts of time and does not pay off for perhaps months from when the work was done. This off page optimization is often the key factor in determining how your site competes with others within your niche and involves building incoming links to your site. An incoming link is a link on someone elses site that appears as a Blue Clickable Link there so if it is clicked on, it brings that person to your page. Google and the other search engines guage people putting your site on theirs as a sort of trust for your site and an indication that your site is an authority of sorts on something. This is especially true if that other site is one that is high ranked by them and in your niche also. You can find ways to "install" your link on those sites yourself sometimes. You do not want to trade reciprocal links with another site as this is an old style that used to work and now actually hurts your rankings. There are tricks to this and you can visit forums on this subject or find a professional SEO person to help you. There is much more to it such as how often to add them and tools to analyze thoses site's rankings, among many other things. Also, google "submit url directories" and get a list of good directories. Yahoo is great, but is is $300 per year. DMOZ is almost the best and free. Others charge small fees or are free and besides BOTW (best of the web), I wouldn't spend too much money, if any. Google and the others also have what is referred to as the "sandbox" which is simply a time period that they almost required in order to rank you well in a competitive niche no matter what good links you get. This is just a brief article to help.
Garry Cooper President/CEO http://firstupseo.com and http://www.fishnfools.com