Start by contributing a majority of your content to other blogs that already have an audience. (Also, create a really kick-ass bio with a link to your twitter handle and blog.) By gaining visibility in an already established community will make it easier for you to gain new quality subscribers and authority.
It is a process that takes time. Don't expect unique traffic to blow the roof off overnight, it just won't happen. Make sure you are consistently publishing really REALLY great content that people want to share. Make sure it passes your internal 'F*ck Yeah' filter (http://onboardly.com/content-marketing/why-you-need-great-content-marketing/#.Usa5NWRDskI) *shameless plug*, and really nurture your community.
Consider other content forms to help with growth, like:
- Slideshare presentations
- guides, eBooks, whitepapers
- webinars and podcasts

Best of luck and enjoy the journey!

Renee's answer is spot on. Trying to guest blog on places that already have traffic will help. Often times you can link back to other blog posts/content you've created if relevant to the article.

The biggest tip is to see content as a framework for many types of deliverables. For example, recently we created an ebook called "Don't Leak Leads: How To Identify Leaks & Get More Customers". http://go.reachlocal.com/DontLeakLeads_request.html.

This content became a series of blog posts, a successful webinar series, multiple infographics, slideshare presentations, and videos. Because we focus so much on education, we also created http://dontleakleads.com. Again all of this was repackaging and rethinking a content framework around how to get more leads.

From a channel perspective, this gave us content across FB, Twitter, LinkedIn, Slideshare, YouTube, and Pinterest and for social media ads, updates, and even pinterest.

Then leveraging a content calendar you can plan when all this happens. Our entire goal is to get someone to fill out a lead form that enters folks into a 21 email behaviorally driven lead nurturing program.

I recommend reading Content Marketing Institute and CopyBlogger.com.

Best of luck!
@MikeDMerrill

Some great suggestions here already! In addition to guest posting, I'd recommend optimizing your posts for SEO. If you're consistent, this will really pay off over time, and you'll get far more bang from your archives as they catch on in search.

Even if you're not an SEO guru, you can take simple steps to improve your SEO. The easiest one is using keywords in your headlines. Lots of other simple ideas in this free webinar: http://alexisgrant.com/webinar-seo/

For some of the blogs we manage, we've also established syndication partners -- big outlets like AOL and Business Insider that want our content and send traffic to us in return. That's something to consider once you've gotten in the habit of providing awesome content.

Good luck!

@alexisgrant
http://socialexis.com

All good responses. I have one question for you. Have you developed a marketing plan for your start-up? A good strategy will identify who your target markets are so you can find the most appropriate channels for your tactics. To capture new business leads, you want to both contribute, and participate in, the "right" online spaces.

All fantastic answers. Another way to help distribute your content is to create a widget that your content feeds into. Then others can place the widget on their blogs and websites. Another idea is to use Google plus. It is a fantastic way to spread your content globally and build an audience. You can also build your own community. Once this builds, you can schedule events, emails, etc. with ease.

Good Luck, and best regards,

Teddy