1. Open your sky replacement picture, go to Select>all, then Edit>copy to place it on the clipboard
2. Open the picture with the drab sky, duplicate the Backgound layer, click on the eye icon of the Background layer to shut off its visibility, and click on the Background copy layer to make it the active layer.
3. Use one of the selection tools, e.g.Lasso tool, to select the drab sky, then hit delete on the keyboard.. The checkerboard pattern denotes transparency.
4. Go to Edit>paste, and the replacement sky will come in on a separate layer.. Drag this sky layer (in the Layers palette) between the Background and Background copy layers. You should have 3 layers at this point.
5. Activate the move tool and position the replacement sky to suit.
The problem with this comes up when one desires to replace the sky where there are trees or other foliage in the picture. I shall offer you an advanced technique for your consideration for this purpose, You will need a picture of a "good" sky - just clouds and sky, nothing elese on it. You can take it yourself or obtain one from another source.
1. Open the sky picture, Select>all, Edit>copy
2. Open the picture with drab sky and trees.
3. Go to Edit>paste. Activate the move tool and using the corner handles to resize and cover over the drab sky in your picture between the foliage and above. Set the blending mode of this layer to darken,
4. Change your foreground color chip to white
5. Activate the Gradient tool, and select the Foreground to Transparent Linear Gradient. While holding down the shift key, drag the gradient from below to the top of the tree line (south to north)
6.With a white brush you may want to gently paint the horizon a bit in order to make it slightly lighter than the rest of the sky.