These are the steps taken in Photoshop:
1. Opened hoop image (the hoop shot against a clear blue sky). Adjusted to taste. Flattened result to one layer (background).
2. Opened cloud image. Adjusted to taste. Flattened result to one layer, then copy/pasted image into the hoop image.
3. Opened bird image. Adjusted to taste. Flattened to one layer, then copy/pasted into the hoop image.
4. All three images are now in one Photoshop document with three layers. Stacked the layers in the following order: hoop on bottom, bird in the middle, cloud on top. In other words, cormorant sandwich. Saved this file as a new name. Closed the other open files.
5. The bottom layer is the hoop image. It's the background layer, and locked. The other two layers on top are open and editable.
6. Turned off visibility of the cloud layer by clicking the eyeball (visibility icon) at the left of the layer icon.
7. Selected the bird image layer. Left the layer eyeball (visibility icon) on.
8. Temporarily reduced opacity of the bird layer to about 50% in order to partially see the hoop layer underneath it. Used the Move tool to move the bird to the center of the hoop. Resized with Transform tool (Ctrl-T) so the bird fits nicely in the hole in the net.
9. Readjusted opacity of the bird layer back to 100%
10. Added a mask (click mask icon) to the bird layer.
11. With a soft brush, painted with black on the mask to remove everything but the bird and some surrounding sky. Used the hole in the net as a guide - treated it as a frame - and painted out all the sky outside the inner net circle.
12. Changed blend mode of the bird layer to Hard Light because it seemed to blend most naturally with the layer underneath it.
13. Selected the cloud layer and turned the eyeball back on.
14. Used the Move tool to place the layer where you I liked it. Resized using Transform tool (Ctrl-T).
15. Changed the blend mode of the cloud layer to Overlay. Adjusted opacity to taste (57%).
Done! Because things were completed in the right order and using the right tools, it took only minutes. When I first started learning Photoshop, this may have taken all day. Remember those piano scales mentioned earlier? There's no shortcut to practice so do your scales.
A good thing to remember in compositing is "do only what's needed" to make the photo look like you want. In this case, the bird was not extracted - the extraction was made around the hole in the net instead. Choice of an appropriate blend mode and opacity then made it appear realistic without undue effort. Same with the cloud layer - the overlay blend mode hid imperfections, and a reduction in opacity brought in just the amount of cloud to add a bit of interest.
The following piece uses exactly the same process to composite a moon shot against a blue sky with a heron shot against a blue sky. Blue was the unifying principle, so again, there was no need for extractions - only a little soft brush masking! Some blend mode decisions and additional texture layers were used to tie it all together.
Ready to try it for yourself? Find a couple photos of your own with simple shapes and plain backgrounds. Start with SIMPLE. Learn as you go, spending time with each tool or button or option until you know it does and how it behaves. Don't expect fast results with Photoshop - if you do, you're guaranteed frustration. Photoshop is a musical instrument, so do your scales and learn your chords.
Photoshop doesn't require patience; it creates patience.