Hi AJ! Maggie, a Shopify Partner here :)
The best way to get a free traffic is to be active on social media - and I don't mean keep paying for ads. Post on social media on a daily basis, make sure to research your content, hashtags, see what kind of content gets viral and follow the same tactics. Team up with an Influencer [this type of agreement shouldn't cost a lot, you will often find smaller Influencers happy to feature your post for free].
Use different tactics on Facebook, different on Instagram and different on Twitter. Interact with your community and engage with followers.
Another way is to work on your backlinks, this is an ongoing process, but one that is going to bring long term results.
Last, but not least, post valuable content on your website [blog]. The morse SEO friendly content you will have, the easier it will be for Google to find you and to direct the traffic to your site, based on what people are searching for.
Hope that helps!
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The best way is to figure out who your customer is and brainstorm ideas on how to reach them. Targeting a niche audience is usually better for stores that have a small budget, since you can tailor your message and find the channels that are very targeted to them. Who did you think of as a customer when you started your store?
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PS: I just wrote, in partnership with Shopify, a guide on how to use data analytics to grow your store. I think it will be useful to you: http://report.compass.co/ecommerce-analytics-guide/