I took a little bit to respond to this question because I wanted to make sure my answer was good. Here goes.
You will need a video capture card/device to be able to stream. As you may know, the one I use is the
Dazzle DVC 100. This is a very high quality composite/svideo capture card. I personally think it's a little overkill for streaming; if you don't intend on recording anything then we can sacrifice some quality for price.
Lurking on other Let's Play forums, I've learned that one of the best
inexpensive capture devices is the
EzCAP. This one costs only $19.99 instead of $39.99 for the Dazzle DVC 100.
Here is an example of the quality from the EzCAP, still good enough for streaming in my opinion.
Whether you go with the Dazzle or EzCAP, we will need to setup it up so that we get a video signal to both the TV and the capture card. We need to split the signal to go to two different places. It is possible that your TV has a TV out ports; use them if you have them. If not, you will need to get video splitters to do the task.
I talk about this in an article I wrote for the Dazzle here. Audio splitters aren't too bad; be careful with video splitters. The signal is different and will be degregated if you use a bad splitter. If you're worried you can get an
Svideo splitter; they cost a little more than composite video splitters. The best solution is to get a video distribution amplifier; that costs another $50.00 however.
Now, we need to stream the video signal to a service like
www.justin.tv or
www.ustream.com. I learned about justin.tv first, but both work perfectly fine. There is a program called the Adobe Flash Media Encoder that will stream the signal from your capture card to the streaming service. (Evilpoptart will hurt me if I don't mention Xsplit right now; it's an alternative program that can do the same thing.) When I get home I'll get a screenshot of my settings I use when I stream.
I stream using my laptop. Here's the laptop's specifications:
Dell XPS m1530
Intel 45 nm Core 2 (1.8GHz)
3GB RAM
nVIDIA GeForce 8400M GS
I would be more worried about bandwidth than computer specifications. If that laptop was manufactured anytime within the last 5 years it should be able to handle streaming. (If you can, give me the specifications so I can give a better answer.)
(Miles, it's called throughput in this case; not bandwidth. Curse incorrect usage becoming the standard.)
Notes:
- Output as 320x240 so there's no interlacing issues
- I'm using Virtual Audio Cable to add commentary. Use the Dazzle Audio Device (or EzCAP)
- To stream to justin.tv or ustream, you need to download a config file for the Flash Media Encoder on your computer. You can get this on your profile on justin.tv or ustream. Then in Flash Media Encoder select file -> open profile, and select the file you got from justin.tv/ustream.
Overall, expect to spend somewhere between $20.00 (just the EzCAP) and $100.00 (Dazzle + Distribution Amplifier) depending on what you buy.
(Are you really going to attempt a Zero Level Pit of 100 Trials?! 
)Last but not leastDo you have an Ethernet cable going to your laptop? Streaming works MUCH better from an Ethernet cable than over wireless. That may be an issue if you don't have an Ethernet cable to your laptop; might have to run cable through your house.
