Backgrounds: Backgrounds are really important, they can make a huge difference in how your edit comes across [ Vibe]. Editing your background is just as important as editing your avatar. You can add objects to it, coloring, people, shadows, light flares, ect. The background colors can also set you up on a color pallet on which to shade your avatar with!
Cleaning Up Your Picture: I think one of the most important things to do before starting anything, is to clean up your avatar... what do I mean by this? Use the eraser tool and go around the edges, make sure the skin and objects are soft and evened out. Fix any glitches your clothes may have; you can do this by using the smudge tool or repaint it by hand. You can also use the smudge tool [ on a really low opacity level ] to soften the skin out so it gives that airbrushed look.
Repainting: Repainting the skin will give the appearance of a more flawless/ soft look. There are many different techniques in repainting skins, different brushes... my best advice is to try different things, develop your own style and learn what YOU like as an independent artist!
Highlighting & Shading: This will make the difference between a 2D image and something that looks more 3D and realistic ♥ For this i suggest watching a few youtube videos on light sources and shadows! But not everything needs to be textbook and perfect... every artist does things differently and has a different vision [ Like I said, experiment ]
Those Last Final Details!!! After you have finished editing, always .... ALWAYS, double check. Make sure to add all those tiny little details, last minute highlights, sparkles, gloss, eyelashes, ect!