In many cases, you have to pay to have your web site promoted on other sites and Internet properties, but some will do it "organically" or free if you provide them with the right type of content. This may involve creating content specifically for a particular venue, such as a video to be displayed on YouTube. Also, appropriate content on your own site may be repeated, mentioned, or linked by someone else. The key in both instances is to have the right type and quality of content presented in a way that allows desirable media to find and recognize its value. Arguably, the most important and productive form of content presentation is "search engine optimization" or SEO, which is discussed more fully here, but below are a few other examples:
Blogs: In addition to web sites, many businesses and professionals maintain web journals in which they periodically post entries on a variety of subjects that may interest their potential clients and customers. Properly formatted blogs are indexed by the major search engines as well as by specialized databases. Blogs that contain interesting and useful content can eventually gain widespread notice and attract lots of visitors.
Videos: As discussed elsewhere, video sites like YouTube offer some valuable advertising space for certain types of businesses, but you can post your own video there as well for free. While it can be hard to stand out among the millions of offerings, it can definitely be done. Even a modest production of useful and/or entertaining material can attract viewers and potential customers.
Press Releases: Tried and true public relations techniques still have great value in the age of digital communication. Alerting the professional news media to significant events and milestones for your organization can result in free publicity, which is always a good thing.