This is a common question when people are starting out. There is an ocean of traffic out there, and you have to get started somewhere.
Here is what I would do if I was just starting a new site.
See whats popular already.
Do a couple searches for your main topics and see what articles are ranking in Google. Then see whats popular on social media. The way I like to do this is a tool called buzzsumo.
Buzzsumo lets you see the most popular content out there and where it is being shared the most. This tool is absolute gold in my book but is a little pricey for a beginning content marketer. They offer 5 free searches every day, and I recommend using them for this tactic daily.
When you find out what people are interested in and actively sharing, check out the articles, and make one on the same topic that is better, more thorough, and longer.
Ok, so now you've made your content. Go to search.twitter.com Search for people that have shared a similar piece of content and direct message then explaining that you say that they shared "XYZ article" before and that you made something similar but is better because of "reason 1, 2, and 3" and ask them to check it out! Say to them "if you love it, it would make my day if you shared it"
That's it! People will respond to these kind of messages most of the time and you will get shares if you spend the time on this.
Using Linkedin for more traffic
Linkedin has become SO much better since Mircrosoft acquired them. I have seen tremendous opportunities open up here and I totally recommend diving in.
The nice thing about Linkedin, is that people are already there with business in mind. It's not an interruption to see your posts or ads.
If you have a network there even better. If not, start inviting your close contacts and see who you might know through your second degree connections.
You may want to build your network even more, I have been testing a tool called dux soup which has helped my linkedin outreach quite a lot.
Every time you produce a great piece of content, go to linked in and go to where you would normally make a post
See where it says "write an article?" click that and add the headline and first paragraph of the article.
At the end add a link that says "read more" to the article on your site.
Linkedin still has some viral capabilities, they still show posts that people like, comment on, and share to all of their connections.
This will surely generate a fair amount of traffic to you site. If you want to take it a step further start joining Linkedin groups in your niche and share the articles there too. You might get kicked out of some groups for doing this but I wouldn't worry to much.
I wouldn't recommend putting too much effort into building a Facebook following. This may be the opposite of what you have heard from most people. But in reality, Facebook really has choked their organic reach.
Above are the results of a recent post I boosted. The dark orange is "paid traffic" and the light orange in organic reach.
If you want to put your effort here, I would just post your article and boost if for $5, if it starts doing well add more to the budget, and be sure your are retargeting properly!
Networking with others online is one of the best uses of your time in content marketing. I would recommend frequently reaching out to influencers in your niche. follow them on Linkedin, Twitter, YouTube and anywhere else, comment on their posts and try to get to know them.
This will lead to more social shares, links to your site and opportunities than anything else. Make a Dream 100 list and start working that!
You don't need millions of followers when your getting started. It simply takes work and knowledge on content marketing.
Keep these tactics up and you'll become a well known figure in your space in no time!