Instagram has a diverse group of users, and those who post “high quality” images only make up a fraction of the users. Companies can use Instagram for marketing purpose, some people use it to show off their children or pets, for others its selfies, food, or lifestyle images, and some people (like my roommate) will only post cigar photos. The point is there are many niches that you may explore.
Personally, I post images taken on DSLRs or mirrorless cameras, and forgo the square crop that is traditionally to Instagram to maintain the 2x3 aspect ratio using an app called Cropic. I would not recommend using a rectangular format if you want to have your photos featured as curators of those accounts tend to prefer the square crop. Most of photos were captured in the RAW file format then edited in iPhoto (early on), Aperture, and now in Lightroom however I will occasionally use the FujiFilm in-camera film simulation and wirelessly transfer images to my cellphone and post to directly to Instagram or do a quick edit on the go in Snapseed.
Selectively like, comment, and follow
Build up your following over time, be patient, and consistently post good work that follows a specific theme or limit yourself to a few themes. Engage people with similar photos with likes, comments, and followers. People with hundreds of thousands of followers are unlikely to follow back, but are often a good source of inspiration. Watch out for people who follow, and unfollow you. This is a fairly common occurrence, yet it is unavoidable and can be frustrating.
Try to keep your follow ratio close to one to one or better. This may be hard in the beginning, but sustainable growth takes time.
*Some hastags have corresponding accounts that will feature your images if you are a follower and user of their hashtag. This can be a fun way to challenge yourself and grow as a photographer.
Tag your photos appropriately
Before using a hashtag, search and see if it is in use. Hashtags with very few photos will not draw viewers to your account. Also, using hastags with thousands upon thousands of post a day will likely result in your image getting fewer views as they will quickly get pushed down the page. Try to keep your tags relevant to the photo you are posting, people searching for macro photos most likely do not want to see your selfie mixed in. I will go through the hashtags I use regularly and like tons of photos in each of the categories. In turn I receive likes, comments, and follows. You may like many to get few in return, but by going through multitudes of photos you will improve you compositional eye and will in turn result in you creating more compelling images.
Also, when adding tags consider asking questions. One of my photos with the most comments was simply a picture of my camera on my bag with the question, "What's in your bag?"
Curate you gallery
Occasionally go back through your gallery and delete photos that you feel no longer belong in your gallery.
Post consistently and do not overwhelm your followers with too many posts at once. I generally post a couple times a week (more would be better), and no more than three posts a day with plenty of time in between.
In the two years that I have been using Instagram I have gained approximately 1300 followers while following about 450 and my most like photo has nearly 700 likes. While this numbers are not astonishing, I am happy with my growth and the feedback that I have received. Remember that it will take time, keep learning, growing, and posting.
Update: The screenshot below reflects my growth in a little under a year from the time of this blog post. I changed my Instagram name to be the same as my website, as I believe it to appear more professional and make sense from a branding/marketing standpoint.