When your site is ready, you can submit it to search engines like Google and Bing. Use the links below to do this.
In general, if your site is already linked to by other websites, you may not even need to submit it to these search engines. They will probably find it themselves by following the links on those websites.
Apart from submitting your site to the search engine, you may also want to consider promoting it in other ways, such as the usual way people did things before the creation of the Internet: advertisements in the newspapers, word-of-mouth, etc. There are even companies on the Internet, like PRWeb, that can help you create press releases, which may get your site noticed by news sites and blogs. As mentioned in my article on More Tips on Google Search Engine Results Placement, you can also advertise in the various search engines. Although I only mentioned Google in that article, since that was the topic of that discussion, you can also advertise in other search engines like Bing and Yahoo!. This has the potential of putting your advertisement near the top of the search engine results page, and possibly even on other websites.
There are also less obvious ways of promoting your website, which you might want to look into.