The following is based on a desire for fame and accolades. PirateCat may well be happy tottling along and writing his story hour without a single peep of encouragement or recognition, but some of us are more human, and greedy. Here is my advice for those of us who are not celestial beings


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Rule 1
Post regularly. This is true of webcomics, story hours, serial novels, half hour television shows, etc. It doesn't have to be daily, it just has to be fairly regular - your audience trusts you to bring the goods on a consistent schedule, and breaking that trust makes them question the effort of checking for updates.
This is particularly important for new readers. Many new readers will read all the way through the archive, but if they get the sense that it may be a long time before they see another update, they won't come back to check up again.
My guesstimate (not a fact

): For the story hours, a short post each weekday, or a long post twice a week, seems to be best for the update-checking rate for most readers (who tend to either check daily and obsessively, or every once in a while in the week). Again, that's NOT fact - it's just a guesstimate based on my own observations.
Other rules
Pimp yourself. This is pretty hard for me. I don't like tooting my horn, and I'm inclined to try to downplay people's expectations of me rather than pump them up... but that's a formula for failure, and so I pimp.
Pimp in a suitably non-jerk fashion. Putting a simple link (or tasteful image) in your sig is a decent way, but don't post in someone's thread without adding something OTHER than your sig

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Post for a while. Especially with a small core population like ENWorld, it's taken me a few months and some 30,000+ words to build up a "moderately successful" 30 or so regular readers.
Get a cheerleader! I lucked out with incognito, who was willing to post near daily encouragement while I was just getting started. Acquiring a cheerleader can be as simple as saying, "Could you browbeat me every time I don't update and yell encouragement occasionally?" Once you get a decent audience, you'll start getting additional cheerleaders.
End each post on a powerful note. It doesn't have to be a cliffhanger (although that is the standard, and easiest, tactic), it just needs to be something that fires the imagination and makes them ask "what's next?". For example, a passionate subplot ending, whether in tears, rapture or wrath, is good. Regardless, your ending has to always leave them wanting more of it.
Find your own style. A lot of my cheer leaders are drawn to the fact that I post interesting (and often very geeky) details about my setting's culture, religion, ecology, etc. That's just my style, and people of similar leanings are attracted to it, so I try to enhance and make that aspect more interesting. Figure out what's best about your story hour, and make it more prominent (then, and only then, shore up your weaknesses).