Either get ready to spend money doing traditional advertising, or go blackhat.
"Going viral" is a myth. The majority of the spontaneous viral hits in the past few years have been carefully planned and executed. Stories get to the Digg front page mostly through coordinated armies of professional Diggers or extensive friend networks. Bloggers take money for undisclosed paid reviews. And don't get me started on email marketing :)
I know because I've had a hand in all of that stuff. I've done it, and it works.
So, you are faced with a choice: whitehat or blackhat?
Whitehat, start doing some traditional marketing- do some basic market segmentation, see what your competitors are doing, target "customers" etc, and then start buying ads- links, paid search, etc or else promoting on the sites your target market uses.
Blackhat, do blackhat SEO- spam blogs/forums, get links, cloak, etc.
Of course, a simple web app may not merit such extensive investment of time and effort, but the difference between a web app and a funded startup is fuzzy at best.