First, make sure that your website mentions the phrases you would reasonably expect an interested party to search for, as regular text in your HTML, not as a picture of text. For instance, if your organization is the Chess School of Lower Funburgh, you need to mention those words prominently on your home page, and they must be actual, mouse-selectable text, not just a picture of text! If you fail to take this step, it will not be possible for search engines to correctly index your site.
Ensuring that your pages contain real text in plain HTML, written with HTML elements that make sense for each piece of content, is often referred to as "organic SEO."
Second, make sure that the major search engines know about your site. As of this writing, Google is by far the most important. You can add your site to Google using their Add URL page.
Third, ask the webmasters of related web pages and sites to link to your pages, and encourage your readers to link to your site. This will bring people in directly, and it will also allow search engines like Google to find you. Just as important, links to your site from other sites are a basic measure of your site's importance that search engines use to decide the rank of your site in search results. In order to benefit from the editorial decisions already made by individual webmasters, search engines do their best to give "real" plain-text links a greater weight than advertising links when evaluating how relevant a website is to a particular subject.
If your needs and your budget go beyond the traffic that simple word of mouth and, eventually, search engine indexing can bring, you should consider purchasing "sponsored links" on search engines. As of this writing, Google sells sponsored links displayed to the right of search engine result pages which are shown only to users who are searching for the exact words that you specify. This service is not free, but it is quite effective, and you pay directly for actual clicks that lead to your site.
A fifth tactic currently observed on the web is the purchasing of plain-text links on other websites. Both users and search engines respond more favorably to plain-text ads, although the major search engines may begin to discount such links as they gradually learn to automatically recognize them. Of course, sites that fail to limit such plain-text ad sales to reasonably relevant products and services, or attempt to disguise them completely as content, may suffer a decrease in popularity and ultimately in ad sales. They could also suffer reduced search engine rankings as search engine companies find new ways to detect and penalize such behavior.