About.com is a terrific resource for someone looking for a how-to article, or top ten list or overview of a particular subject.
About.com used to be a "directory" like the old Yahoo Directory. Its business model has changed over the years, and now it has "Experts" (aka "Guides") who create and control various categories of information within About.com. But it no longer acts as a directory. For example, there's a section of About.com concerning candles and soap, (candleandsoap.about.com), and there's a very nice Expert for that section (David Fisher), who is quite knowledgeable about soap and candlemaking. He writes all the articles within that section of About.com.
Other Experts at About.com write about their own areas. About.com is always looking for more Experts and if you're interested in and have knowledge and skills in one of the areas up for grabs, you can contact them about it (links to "Write for About.com" are at the bottom of any of their pages.)
A link from About.com to your website, mentioning it as a resource of one kind or another, from the appropriate section of About.com, is a terrific link to obtain. Note that links to external sites from about.com are "rel=nofollow", but even so, the "citation" (reference to your website) will still help your website.
There's no way to "list" your site or "request a listing" because About.com no longer offers that. (Because About.com is no longer a directory!) Instead, you can get in touch with the Expert over the area covering your website, and start a conversation. Mention that you have a website about your subject, something unique about your site, and see what develops. They are often looking for new things, clever ideas, and helpful sites about which to write.
Keep it real! If you're trying to hype an affiliate site of some kind, or a website of little value, it's not worth your time or the Expert's time to contact them.
These About.com guides/experts are busy, so keep your contact simple and direct. It pays to be polite, and to have something truly helpful on your website that would actually interest the Expert and the readers of About.com.
Over the last decade we've gotten some terrific links for our clients from about.com, through actual communication with the Experts/Guides over many different areas.
Note that "Sponsored listings" (the ads at the top and bottom of their lists of articles when you do a search) on About.com come from Google Ad Words.