Natural, or "organic", links are not special URLs as the name suggests to many people. Instead, what search engines are looking for are links to your website or article that are generated through general interest, not traffic mills.
Ways to generate natural links include many of the same ways you foster good net etiquette in the first place. Leave relevant, useful, information-rich comments on others' blogs that genuinely interest you and relate to the content you produce on your own site. First link to other sites that produce quality, relevant content and then, if those site owners find your content to be equally relevant and useful, they are likely to link back to your site and share your content with their readers.
A natural link happens, well, naturally. You can increase the likelihood of being linked to by reaching out to other bloggers and site owners, but you shouldn't just go posting links to your own content on promotional sites. Search engines are adapting to recognize the difference.
Social media is a great source of natural links, so another great way to secure them is to share your content (in moderation) with friends and family who can, in turn, share it on their social network profiles with their friends. That's by and far one of the best ways to get high quality, natural links as search engines look upon Facebook, Twitter and Google+ links very favorably.