The very basic is:
Make 2 new document : One document bigger than the other.
Drag the smaller document into the bigger document, and hide the bigger document background. You should now see grey and white little square.
It's the transparent background. Save it as a png and the grey/white square won't appear on the final product.
To add shadow, simply go in the blend option.

That was for the basic. Not so easy to use but I learn'd it this way

For the easiest way to do it:
Make a new document.
Double click on the background layer. Press Ctrl + T then resize to your liking.
Go in blend option and select shadow.
For curvy border use the smudge tool.
