There are lots of things you can do when you take a picture. Aside from the obvious focus and framing, you can fiddle with the camera's many settings. Things like white balance and exposure, tweaking the settings for things like contrast and sharpness, and you can pick one of the camera's built-in effects. Or you can shoot in raw and probably end up with something that looked like the camera's JPEG output. Some may put the picture into a photo editor and fiddle with it until it's "photographically correct."
But, in most cases, the picture isn't finished. Sometimes I look at one of my pictures, straight from the camera, and it looks pretty good. Perhaps I should use it as-is. But I'll put it into a photo editing program and, in a matter of seconds, I can see how wrong I was. One thing that helps is to have an editor that lets you switch back and forth between your current version and the original version. It's good to have the ability to see your progress and make sure you haven't gone too far.
Cropping - To position your subject, to isolate, to zoom in, to improve the framing, to remove unwanted detail, to make the proportion of your picture more interesting, to balance the items in your picture.
Simplifying - Removing extraneous detail or taking areas with distracting detail and darkening them or putting them out of focus.
Accenting - Sort of like simplifying, but with the emphasis on forcing your eye to a certain part of the picture. Things like eliminating distractions towards the edges of the picture.
Transforming - The pictures above show how the boring summer appearance of the original was transformed into a warm, glowing autumn sunset.
You need to have a feeling for playing around, exploration, and experimentation. ("I wonder what this slider does. What if I push it the wrong way. Hmm...") It costs nothing but your time. Certainly more fun than watching TV, and more rewarding as well.
As you evolve your new variations, save each one with a new filename so you can see the progress. It also allows you to backtrack if you've gone too far. Make sure to save each new variation in TIFF format.
One final word of advice. Finishing a picture is like putting on makeup -- you have to know when to stop.