If you hadn't already guessed, the Web is not going to be the wellspring of wealth that a lot of people assumed it would. Some people will get very wealthy, but other people will earn nothing, and, in the nature of business fail and go out of business.
However, if your goals are a bit more modest, it is not unreasonable to expect your Web site to bring you some extra cash. Perhaps pay for the Web service it's running on and take your family out to eat once or twice a month. Perhaps more.
Affiliate programs are a simple way for you to get some extra cash coming from your Web site. An affiliate program is where you partner with another company, usually an ecommerce company, to sell their product from your Web site. For every product you sell, you get a portion of the proceeds. The best known affiliate program sells books for Amazon.com, but you can sell anything from car ads to fishing flies.
Many sites have advertising on them, and they are another way to add a revenue stream from your Web site. The money from advertising comes in two ways: first from the number of people who view the ad and second from the number of "click-throughs" on the ad. Basically, if your site gets a lot of hits (and so a lot of people will see the ad) it will get a better rate for advertisements. But even sites that have lower hit rates might have high numbers of clicks on the ad, and this will get you a better rate as well.
Advertising can take the form of banner ads, which usually cost a lot, or just sponsored links. You can see examples of each of those on About.com as well. The banner ads on the top, bottom and sides cost more than the sponsored links on the bottom, and they each bring in different amounts of revenue.
There are lots of articles and information on how to raise money from your Web site. If you're interested in advertising, look at my Advertising resources. Affiliate programs (also called Associate programs) are listed on my Making Money resources page, as well as information on how to get started with associate programs and advertising on your site. If you are ready to move on to more advanced money making, then you should read my ECommerce resource page.