There are a few ways you can do this:
1) Search Engine Optimization:
This is making your website more obvious to a search engine so that you will appear higher in searching ranks etc.

2) Paid Advertisement:
There are site you can buy advertising space from. The bigger the site the more likely you are to have more visitors but bigger sites charge more.

3) Free Advertising:
Such as adding the link to your signature and posting around a variety of forums is one suggestion. Another is to have a blog, apparently that is good for gain traffic to your site if it is popular. Also asking site owns to affiliate their site with yours, they add your link to their site and you add theirs to yours.

Good luck!