Draw a gradient on your layer mask. Hold down your Control key (this ensures a straight line). Click and hold down your left mouse button on (or at some point above) the horizon line and hold down your left mouse button. Drag your mouse pointer to some arbitrary point upwards; you will have to experiment with this to see what works better for your photograph. Release your left mouse button. In the Layers dialog, right click on the "Background copy" layer and go to Show Layer Mask to ensure that you've done it right. Do the same again to turn off the display of your layer mask.
How to Make Skies Beautiful with GIMP Picture 5
Set the layer mode to "Soft light" from the drop-down "Mode" list. You will notice that the contrast and colour of your sky has improved. This is what you want. We'll call this the "soft light layer" from here on.
How to Make Skies Beautiful with GIMP Picture 6
Duplicate your soft light layer to taste. Zoom to 100% on your photo (View -> Zoom -> 1:1). Then, in the layers dialog, right click on your soft light layer and go to Duplicate Layer. Do this until either you're either happy with it, or until you start seeing large blocks of colour (when you hit the latter, this is sensor or film noise taking its toll).
How to Make Skies Beautiful with GIMP Picture 7
Merge your layers by right clicking on any layer in the Layers dialog and going to Merge Visible Layers. Hit "OK"; none of the options are relevant here.
How to Make Skies Beautiful with GIMP Picture 8
Kick up the saturation in the sky a little. This is optional. Use the freeform select tool (hit F) to loosely select the sky. Go to Select -> Feather, use a Radius of roughly 1%-2% of the height of your photo in pixels. Go to Colors -> Hue/Saturation and slide the Saturation slider over to the right to taste. As earlier, it might be best to zoom to 100% in order to ensure that you're not bringing out too much noise in the process. Hit "OK" when you're happy with it.
How to Make Skies Beautiful with GIMP Picture 9
Recover the shadow detail from below the horizon. You can skip this step if you used a neutral density filter on the sky. Duplicate the bottom layer and add a layer mask, as we did in steps 2-5; except this time you want to do it backwards by drawing the gradient starting at or just above the horizon line, and ending at some point just below the horizon line; the end result is that the ground will be in the white area of the layer mask, and the sky will be in the black area. As before, you'll have to experiment with this. Set the layer mode to Dodge or Screen. Duplicate it to taste, then merge them, as before.
Do any other processing that you see fit to do. In our example, the sky was crudely de-noised a little with a selective Gaussian blur (Filters -> Blur -> Selective Gaussian Blur), then the area below the horizon was sharpened (Filters -> Enhance -> Unsharp Mask), and finally a single pass of Harry Phillips' "tone mapping" script was applied.
How to Make Skies Beautiful with GIMP Picture 10
Admire the finished result. Or don't; go away for a few minutes, come back and compare it to your original to see if it really was an improvement. Chances are good that it was; but it doesn't hurt to go back to the start and experiment with different layer masks, and so on.