At first I want to mention that I shot RAW and process the final results in-camera afterwards to get the final JPG file. That gives me more control about the applied color profile, sharpness and other aspects of the image. Maybe the image needs some shadow recovery or reduced highlights. You can't do that with a JPG file because there is no headroom in it that allows that kind of editing.
I use an android phone in conjunction with Snapseed. There are no other apps involved because I want to keep the editing process simple and get the most out of one app instead of creating more clutter. Snapseed is an easy but powerful application that has a wide range of tools from simple adjustments to more sophisticated functions like a tone-curve or perspective correction. With the last version you can also store certain looks for later use what saves you some more time to archive a certain look.
Most of the times I only adjust the tone-curve and the saturation, but sometimes I also use the control point feature to add more structure to certain areas or darken the sky etc. Snapseed is capable of opening large JPG files without a problem. The saved results look great for being edited on a smartphone without calibration on the go.
After editing comes backup which is an important thing to do. If you have a google account or something similar you can use a special app to backup all of your photos when a wireless LAN is in reach. It's good to mirror your images to a different place when you are on a longer trip, because your camera can break or got be stolen. You can buy a new one, but the photos are gone forever! So just set-up one of the many apps that offer a backup feature and always seek out for a place with free WiFi. If you're out in a desert then try to put the photos on more than one card etc. to get more redundancy.
Upload & done
After the final image is saved I share it directly via Instagram. What I like about this process is the simple approach that is not so much focused on the details. You can edit your images in a nice coffee place and on the train. It feels a bit like back in the instant film days where you started to play around with the medium. And when you're on a long trip and want to travel light, this combo might be the best for you to save some space in your Rucksack.