Basically it's a combination of promotion/advertising in old media, promotion in social networks, SEO and other marketing magic (aka What Would Don Draper Do). The downside is that this requires a lot of money to do so you either need to have the money on hand or know somebody who'll provide it as venture investment or a business loan.
Now, you can go smaller and grow. Basically, you have to find something you can rank for in terms of SEO and/or isn't too expensive for PPC ads. If it's a topic people like to talk about and are passionate about, you'll get regular visitors, readers and commenters/posters (aka free content providers) in most cases. It can grow quite big over time. Consider how well StackExchange has done from essentially a small beginning.