Fan fiction authors are frequently concerned about increasing readership of their creative writing. Sometimes they are driven to stroke their ego through traffic; sometimes they'd like more feedback to improve their writing. Writers often want to increase their name recognition, too, in advance of publication of non-fan original works of fiction.
Whatever the motive, fan fiction authors need to understand the existence of a critical ratio -- the comments per post ratio. Only a small percentage of persons who read a blog post will actually take the time to comment. This percentage is even smaller than the number of visitors; remember that some traffic to any URL is accidental or drive-by and will only skim, not read any content at the URL.
This same ratio exists for ANY site on the internet, whether a Facebook page or a Twitter account. It also applies to any works of self-published fiction, fan or otherwise.
To understand more about this ratio, see this article: Ratio Analysis for Bloggers 2-Comments per Post Ratio
It's also important to understand that even the very best of products, from Apple brand electronics to fast food hamburgers, will not become popular if they are not promoted. By promotion we mean placed in a way that potential customers see them, become aware of and interested in trying the products. Companies use a combination of tools to this end, including advertising and placement of product in key locations; it's no accident that popular cereals, for example, are on the grocery store shelves right at your eye level where you can readily see and reach for them. That's a deliberate effort to make the product available to you.
Yes, you may already have self-promoted your work through your own blog, Twitter or Facebook account. If your readership at those sites is proportionally small, this will not increase traffic or widen interest among new visitors. You'll have to stretch a little more for effective promotion.
In the blog world, promotion can take the form of links at other blog and websites, including actual advertising. It may also take the form of recommendations by key personalities who have popular blog/websites.
If you are trying to increase readership of your creative writing, whether works of fan or original fiction, you'll want to identify sites which are geared toward promotion of your work. In the Twilight fan fiction fandom community, the following sites are frequently used to promote fanfic:
Another method of promotion is posting about your works at community sites popular in the fandom, like A Different Forest. Submitting appropriate works as requested by other fandom sites may also help, like Perv Pack's Smut Shack or The Lemonade Stand (in these two examples, content is for mature audience and works must be M-rated).
One other option is participation in popular awards as the awards sites will help with promotion of your work. Two examples for the Twilight fan fiction community are:
Authors may also want to consider participation in charitable events like Fandom Gives Back. By contributing a small work of fiction under the event's guidelines, authors may reach a new and wider audience and increase readership of their other earlier and future works.
Take careful note of the most popular works of fiction and their authors. How are those works and writers being promoted? They may offer additional education about effective promotion through a little research into their outreach efforts. You may find that some do not have any presence on Facebook and/or Twitter but only have a fan fiction account. Look carefully at what works to make them popular.
Lastly, it's important to remember that readers want to experience quality works and will help increase readership by word if they enjoy a particular piece of writing. As an author it's important to remember that if you focus on the quality of the content itself and treat reasoned critiques respectfully in order to improve your work, readers will be more likely to both enjoy and assist in promoting your work.
There are untold numbers of unsuccessful products pulled from the shelves which didn't make potential customers happy enough to buy the product, in spite of massive ad campaigns. Works of creative writing may be no different than these commercial products.
Writing purely for the sake of increasing traffic isn't enough to actually increase traffic; readers want something worth the investment of their time, whether to stop and read or make the greater effort to comment. Give them real value, something worth their time which piques their interest and entertains them -- or all the promotional efforts in the world won't make a difference.