Just having a website is one thing. Getting to show up in a search is something else.
We call it Search Engine Optimizing. In order for your website to show up in a search it needs to be relevant to that search. For instance, if you make a website that has to do with your business because you want to get customers, you need to think of how a potential customer might search for you. Figure out what words a person searching for you might type in to Google or Yahoo. Those terms people would use to look for you are called “Keywords.”
Then you need your website to be relevant to those “Keywords,” so that the search engines will consider you as a viable result. If you are just doing this for your own personal website (not a commercial venture) then it can be fairly easy as long as your name is not too common. The more unique a name is the easier it would be to get it to be relevant if someone where to type it in exactly. If your name is John Smith… well lets just say you may be at it a while before you rank well.

Focus on your content, use rich keyword in both title and content. And get backlink from quality site

Here is a post telling how to get your blog or website indexed fast in Google and other search engines. You should give it a read.

Daily Technology Tips