Media is ever changing so there is no one way or one channel to do this, no set and forget formula!

Best to create phenomenal content, have a media schedule and repurpose your blog, vlog, post or article.

Share it with groups, quote key opinion leaders and select media your target audience interacts with.

Find brand alliances by affiliating and guest posting, speaking etc with people who have the same audience.

Interview people who already have followings, Google Hangout, Podcast and share the interview, create a series.

Step 1 is decide what your brand story is, then schedule a marketing action plan (weekly or monthly topic), then go for it!

That's a great question but the answer would really depend on your product / service, target market, funding and a multitude of other parameters. If you want to do this relatively quickly and have a decent marketing budget then certainly paid media would be a very safe bet.

I would focus on a range of digital channel that would maximise reach to your exact target audience and implement a few measurement tools to evaluate the most cost effective media sources and audiences. 

There are some fantastic ways to do this utilising Programmatic TV ads, Digital Billboards, Video and Display channels to reach millions of people and create mass brand awareness fairly quickly.