I. Chrome OS vs. Chromium OS
Like the browser, the OS has two variants. Chrome OS is what you will find on Chromebooks. It is based on the open source Chromium OS, but has a few additions. The most important are built in plugins for mp3, pdf, flash, and automatic updating. You cannot install this "full" version, you can only get Chromium OS.
II. Getting Chromium OS
You can build it yourself, but this is pretty hard. You need a medium- to high-end desktop running the old LTS version of Ubuntu (forget which one it was) or a Mac. Or install Ubuntu in a virtual machine from Windows. I have not attempted this.
Instead, there are a few developers who have made builds of Chromium OS that you can flash onto your machine, similar to other Linux distributions. Hexxeh and Arnold the Bat are two sources for plain "vanilla" builds. If your Wifi chip does not have drivers in the standard Linux kernel you will probably not be able to get it working, as you cannot install packages onto Chromium OS the way you can with most Linux distros. In the past, both Hexxeh and some guy at Dell have built versions with additional Wifi support, but both have ceased work on this (last builds were many months ago). Since you cannot update Chromium OS from within the OS, i.e. you have to reflash the entire OS to update, I do not recommend these old builds. For my laptop, I actually bought a new Wifi chip to fix this problem. They are cheap ($5).
If your touchpad doesn't work at first, try plugging in a USB mouse temporarily, and you can probably edit some system files to get the touchpad working. Arnold the Bat has advice on that, and I have done it so I can help troubleshoot if you need it.
Edit: Doug Anson from Dell has updated his build as of 2/20/2013. This will be a good option for people with Broadcom WiFi and older Synaptics touchpads.
I haven't tried yet, but have been thinking of doing it one day. I'd like to be able to dual boot Chromium OS and maybe Ubuntu or one of it's variants (Linux Mint, Linux Lite). The other thing I thought of is using Puppy Linux (fastest OS of anything out there) with Chromium Browser.