I guess I count as a successful serial. I have a good few readers - 3,500 unique visitors on a good day, 18-19 thousand views. (This is a fairly recent development, as I sat around 3,200 visitors and 14-16k views through July/August).
I don't use social media, excepting reddit. I focus on the writing and let things spread largely by word of mouth. Above all else, this is my advice to you (and anyone else). That lame line, 'if you build it, they will come'? You need content before you can have readers.
My stats: http://oi44.tinypic.com/o8t7r7.jpg
Note how many months (6- went by where I had virtually no viewers. Not a concern. Not a cause for worry. I didn't give it a second thought because, going in, I expected no viewers at all, virtually no comments. I was pleasantly surprised, thrilled to have any reviews at all. When I started getting raving reviews (like Gavin's), my mind was blown.
It's continued to be blown since. I'm sure you can see some points on the graph.
But what the graph doesn't show is the output - I'm essentially writing a book a month, and have been for a while. My story is 1,500,000 words long (and change).
Build it, they will come. I stress consistency and frequency as well. I haven't missed an update. For readers who've made Worm a part of their routine, I've not given them a real excuse (beyond points in the writing that may have crossed a line for them, tastwise) to stop reading. No breaks where they can go find something else to read with their tea two or three times a week.
In terms of spreading the word, some of the more helpful areas have been:
? Webfictionguide. I owe Chris/my reviewers a lot. Get involved, help others out. I wish I could review more myself, but it's worth reviewing so you help bring attention to other authors in turn, and this may get you more reviews/attention as a consequence.
? Readers mentioning the story on forums. So long as discussion is happening, it's a steady influx of viewers, as people come in to see what others are talking about.
? Fanart, fanfiction. I can see why people would be leery about having people make stuff based on their own works, but I've written a story that lends itself to fanfiction and I've given permission (even encouraged, carefully) for people to make the stuff.
? TV tropes - not just being there, but having a mess of links. I'm forever grateful to one reader for adding extensive amounts of my stuff to the site. People wiki walk their way to Worm with some regularity. One of the big leaps in the image linked above is due to TV tropes (March/April 2013 - pretty much doubling my viewership).
? Reddit - I get involved in the community, offering advice on writing subreddits and sharing honest input on my own experiences. People will often ask for a link to my story, which makes for new readers.
But above all else, write. It's the solution to all your problems. Write, write, write.