One great way to learn how to take and process better photographs is to learn from professionals, and for many of us time and circumstance precludes dropping everything to do an internship with a professional photographer. Fortunately, there are pros like Jessie Webster -- who runs the "Sweet Thing" blog -- who are kind enough to share their photography workflows with the world and help make our photographs better.
In a classic post from July 30, 2013, Jessie outlined her photo editing process for Instagram. Yeah, I know -- I was thinking "a process for an Instagram photo?" too. But that's what spells out the difference between a professional photographer and someone taking snapshots with an iPhone.
Jessie started with a self-portrait taken with TimerCam (free or US$1.99 for the pro version) and then ran it through VSCO Cam (free) to add a filter, lighten, straighten and crop the photo. Next, she moved the photo to Afterlight ($0.99) to add clarity and sharpen the image. Finally, the image passed into Touch Retouch ($0.99) to remove some distracting foreground rocks and sticks before being uploaded to Instagram (free).
Be sure to check out Jessie's tutorial on Sweet Thing for more details.