On Instagram I post only photos taken with my phone 4(now s!).  For those photos I use the iOS app Afterlight extensively.  As of this article the app is only available for iOS although I hear rumours of an Android version coming soon.  I hope they're right - it's truly a great app that everyone should have access to use.

Basic Workflow

Highlights and Shadows

After opening my file I typically go to Image Options tab (denoted by three sliders) and see how much room I have with both highlights and shadows.  If I want to get specific with lighting in this way I'll open the file in Snapseed and use the Local Adjustments to change the brightness as needed.  Much of the time these controls suffice.  They provide just enough flexibility in drawing out contrast without going overboard.

Presets

If I'm happy with the highlights and shadows I'll typically hit the presets tab to see how the photo will look as black and white and with greater contrast.  I generally have a sense of what kind of mood I'm going after with an edit but it's always good to see how it looks with a quick preview.  Sometimes I'm (pleasantly) surprised by a preset and choose to go with it.

Crop

I'm personally fond of the 8x10 crop - and not just for portraits.  Not quite sure how to explain it otherwise ... it just works for me.  You may have other favourites for completely other reasons.  Choice and freedom rock.  I'll start with an 8x10 crop and, if for some reason, it's not working out I'll try framing with different (or the default) aspect ratios until I get the one I want.  80% of the time I'm with 8x10 or simply the out-of-camera (3x2?) ratio.

Borders

When posting to instagram you need to fill in the gaps to make it a square or else the app will force you to crop further.  This removes any consideration you made to composition.  Personally, I like to have that control.  You can put on borders at any point - they do not affect the processing of the photo as they are applied during export.

Saturation

I tend to reduce the saturation on my images by about 10%.  That's just me.

Clarity

it's always fun to see what the clarity slider brings to your image.  I f i do apply clarity rarely will i got above 25-30%.  Like sharpening, it can get really dodgy really quickly.  Moderation is key.

Sharpen (always last!)

My final step is to sharpen the image as required.  I'd say I do this about 30% of the time.  It's easy to go overboard with sharpening.  Moderation and restraint are key here ;)  How do you know when you've sharpened too much?  You'll start to see edge artifacts and halos around objects.  Things can go downhill very quickly.

There you go - a simple Afterlight workflow.