Create content that pulls people in
There are several content types: personal, educational, entertaining, sales. It helps to have ideas for each so you can plan. That way you reach a wider audience and get more comments and likes.
Engage with your audience more
Join discussions not only under your posts but also under bloggers and competitors in your niche. Write in context—don't just drop a plug for your account; that's spam and it backfires.
Don't skip hashtags
Build a set of hashtags that fit your niche. More and more people follow hashtags like they follow accounts, so it's extra traffic to your profile.
Use popular locations
People often forget to add a location to posts. It matters: find popular or relevant locations and use them.
Don't forget other social networks
If you have a following on VK, Facebook or elsewhere, tell them about your Instagram. No need to be shy—cross-promote.
These tips aren't a silver bullet; experiments often work well too. Combine them with tools you already trust.