To elaborate on pdurrant's reply, even if the book is free you can't download from Amazon without an Amazon account, so if you don't have one you need to open one. Next, you need to establish a one-click payment method either by associating a credit card or buying an Amazon gift card. For more info about this requirement, see this customer discussion thread on the Amazon forums:
http://www.amazon.com/forum/kindle?_...TxBULDTN0JLOX0
Once you have your account set up, you need to register a Kindle device or Kindle reading app to your account. If you don't have a Kindle device, download one of these apps depending on which device you plan to use to read your Kindle books:
http://www.amazon.com/gp/feature.htm...cId=1000493771
Once you have an account and a registered device or app, you can browse and download Kindle ebooks from the device or app or you can download to your pc and transfer by usb.
If you plan to use Calibre to store and/or read them, you should download them to your pc then add them to your Calibre library. It may sound complicated if you've never done it before, but it's all very simple and easy. Enjoy your Kindle books!