Although it's true that there are many ways to promote your writing online, it's equally or more important to make sure that your writing is able to promote itself. This is what's called your article's potential to earn money through an extended period of time, an "indefinite-earning" article.
You can promote your writing by going to forums, signing up to be a member, and put a link to your writing somewhere on your "signature" line. This way, as you participate in the forum (and do not just use the forum to solely market yourself; the moderators won't appreciate this), people will hopefully click on your link. Other ways include: using Digg (though it's quite difficult to use this successfully unless the topic of your writing is very specific and popular); social networking sites (such as Facebook or MySpace, though this is also relatively difficult to do, unless you have a lot of exposure); blogging (which is one of the best ways to bring exposure to yourself and your writing, but you must know how to market yourself and find ways to get new viewers constantly); and another webpage of your own, whether it's a business or personal page (though different from a blog). These are only some of the ways that you can promote your writing, but notice that there is always a "ceiling" to what these methods can do. They won't work by themselves; so, what else is needed?
An "indefinite-earning" article is one that is both popular and one that people will need to read, whether it's today or next month or next year. This is the article that's going to attract new readers everyday, thus earning you money now and in the long run. These articles are difficult to write, and they happen few and inbetween. But, what's most important to remember about them, and what's unique about them, is that they promote themselves. They do about 80% of their own promoting, because they are well-written and have SEO's and key words that will show up in most search engine searches. This is the kind of article that, whether you promote it or not, will earn you more money than the one below it.
I wrote an article a few months ago that I didn't think would earn me any money at all. It was about how to cut side fringes (a hairstyle). Now, although this article did not earn me a hundred dollars in a day, and neither did it earn me $1,000 in two months, it opened my eyes to the possibilities and potential that I had through my writing. If I could only write articles that were like that: it was search-specific, it was popular, and it's something that people will search for over and over again. So, although it didn't earn me a whole lot of money, it is still my highest-earning article to date. And, most important of all, I did no promotion. This article promoted itself.
So, if you want to promote your writing, start with the way you write and what you are writing about. As it has been said, write about what you know and that's what you'll write best. If you think that your knowledge will be able to help others and make them think, then share that knowledge. You never know; it might just start that "indefinite-earning" article that every article-writer dreams of.