2012-01-22 Since the initial writing, there has been a new virtual machine released, which streamlines some of this. This post has been updated to reflect these changes.
First, you'll need to download and install VirtualBox, a free VM environment (as of this writing version 4.1.8 is the latest).
After you've installed VirtualBox, you will want to download the VirtualBox extensions.
Then, you'll need a copy of the Raspberry Pi virtual machine. The developer who has created the VM has put a torrent to the VM here (it's 1.9 gigabytes, so local hosting is... tricky).
Don't have a torrent client? This one seems to be a good mix of usability and low-invasiveness:
Once you have VirtualBox installed, open the zip and put the VM image (RaspberryPi-Development-v0.2.ova) somewhere convenient. You should be able to just double-click the ova file to get the VM imported.
Start the VM, click the Raspberry Pi Developer account, and login with a password of:
Poof, before you know it: A Raspberry Pi dev environment running in a VM.
Next up, compiling and running "Hello world".