Viral marketing is the practice of having other people promote your site. This leads to other people finding it and promoting it, and so it spreads like a virus.
Now, don't get me confused. This isnt going to be a piece of cake, either. But once you've set a good viral marketing plan rolling, it's better than promoting your site 'the old way'.
Now, how to go about getting people to promote you...
First, write a free tool, and make people who use it link to you. This is what got the people at statcounter their PR 10. Now, I'm going to assume that you can't write a free useful tool easier than normal marketing, so lets go on.
You could also try writing articles. Write them and submit to 100 article directories, the ones that give out free articles. Wait, why give out content? because of the link you can put in the 'resources' box. That's 100 links to your site from the directories. But that's the tip of the iceberg. Assume that 10 people use the article in their own page from each directory. You now have 100 * 10 = 10000 additional links, plus the 100, meaning 10100 links to your site, and all you worked for was 100.
Also, you could have good quality content on your site, have things people will come back to, games and free information are very good. This will be slower than the articles, but will also help in the long run, because who cares about 10100 links if everyone who clicks hits their back button?