late January 2013
VMware creates ESXi and vSphere for use in creating and managing virtual machines with guest OSes on any nice piece of hardware you've got.
Start here: vmware.com. Look to sign up with WMware, My VMware.
You can sign up with VMware to use their ESXi and vSphere Hypervisor for free. Once you sign up, you can download ESXi from a page they give you a link to. That page is called "My VMware".
You install ESXi on a piece of hardware with no OS installed on it. It becomes the virtualization piece atop which you install guest OSes. When you install ESXi, it ultimately gives you a URL you need to use from a browser on the Windows host from which you'll perform administration of VMs.
You administer all of this from a Windows box. I run a (legal) copy of Windows 7 Profession 64-bit in a Sun VirtualBox. When I type the URL given me by ESX into a browser running there, it engages a download and installation process by which I can get vSphere running. Here is an illustration of what I see when I go back in (after losing my Windows box) to download it again. (It's the last download button shown.)
At some point, running vSphere, I'll be asked for a license. It took me a while to stumble upon it. Here's an illustration of where I found it (on a page listing my VMware downloads, which is where I was able to get the ISO I used to install ESXi in the first place). This might help you locate it.
At this point, my interest is really in VMware vSphere. Please see the following links for very practical details on my experience.