First you need to install Ubuntu. Download the iso image from the following website:
Once you've installed it, you might want to install an appropriate graphic driver
that supports 3D acceleration (nvidia or ati depending on your hardware)
Then you can will install beryl which is a windows manager that creates
all those eye-candy effects. I might be wrong here but the beryl project has
been discontinued and merged into compiz-fusion and compiz-fusion might be installed by default
on ubuntu 7.10. I'm not sure though.
So download your iso image, install it on your new computer and let us know how it goes.