Can someone please explain the process or point me to the instructions somewhere?
I DON'T have my Kindle yet, but it is on order.
There's lots of information on Amazon under
Kindle support.
1) If I understand correctly, I can use the Kindle to access Amazon and order books directly from my Kindle - is that correct?
Yep.
2) More often though, I think I'm likely to find a book on Amazon while using my PC. If I purchase from my PC on Amazon, does the book go directly to my Kindle? Is this automatic - like just turn on the Kindle and turn on Whispernet? Or does the book go to my PC and then I have to transfer it from my PC to my Kindle?
You can do it either way. When you purchase, there is a drop down menu to specify where to send a new purchase. You could send it to your Kindle via Whispernet (and it will download the next time you turn Whispernet on), or download to your PC and transfer it via USB.
3) What is the process to buy a book from a source other than Amazon? Can I use my PC for that?
Depends on the store. If you're buying (or downloading freebies) from other sources, first make sure that they are DRM free. Mobipocket is the best format for Kindle, but other unsecured formats can be converted to work on it.