I would start by identifying relevant content publishers or potential partners in your vertical and contacting them to discuss how you could work in partnership, some people may be happy to have some free content and others you may have to barter with. You will probably have to invest a fair amount of time in establishing these relationships.
A word of warning, be wary of targeting keywords in these external articles that will be high priority keywords for your website. If the content is being published to a authoritative domain you may struggle to rank above these articles even when your domain authority increases.
I don't know if you have budget for PPC but this can be a great way to drive traffic to your site whilst your organic presence is in it's infancy.
Hope this helps.