I have not succeeded with any of it, yet. I just found the project thanks to digg.com and am planning on giving it a try tomorrow. However, I feel I understand enough to answer your questions:
The wiimote (wii remote) connects to your computer through your computer's bluetooth connection. Most laptops sold these days are sold with bluetooth or the option to add bluetooth for a fee. If your computer does not have bluetooth, you can purchase a bluetooth "dongle" for relatively cheaply on various places on the internet including ebay.
So that the computer knows how to connect to your wiimote, download and install this application:
link.com/file.exe
In all of these tutorials, the PC is connected to the television or projector. I do not know of any way to use this hack without using a computer.
As the above poster said, you do NOT need to even own a wii to use the hacks. All you need is a wiimote and a set of infrared lights (which is what the wii sensor bar is). If you do have a wii and do not want to keep your wii powered on just to use it's sensor bar, you can just hack the sensor bar to accept another power source, or use batteries. I've seen numerous tutorials on how to do this- a quick youtube or google search should provide you all the information that you need.