It's a long process that took me forever to figure out, but here are the basics. I'll probably write a blog post about it.
Pin something, get a couple of repins, then repin that to a very popular community board (it takes work to get invites to those with followings of 150,000+). Follow, like, and comment (sincerely) on the pins of people who repinned your pin.
Rinse and repeat. On the average day for a newer site/account I'll drive between 1,000 and 2,000 visits and get about 100-150 new followers. The average product I pin will get 20-50 repins on day 1. But the crazy part is, as you mentioned, that all compounds over time.
The most important piece of information I'm willing to share is that if I could advertise on Pinterest I would switch all of my clients' ad spend from Adsense to Pinterest today. Promoted pins are going to be worth mad cash.