To begin, clean the chain. Using whatever solvent you have on hand (orange degreaser, Palmolive Oxy, paint thinner, gasoline, etc.), soak the chain in it to get all (or most) of the grease off. I cut a discarded 1 gallon plastic jug in half with a box cutter and used Palmolive Oxy. That stuff is amazing - next time you're working on your bike, or heck, making this chain whip, try washing your hands with this stuff - works great! Set the chain aside to soak.
Now saw off a 12" to 16" piece from the 1x1 piece of wood you've found. I'm not sure the official length for most versions of chain whips out there, so create a piece that looks right to you. You don't want too long a piece of wood, as you will want your hand close to the cassette to control the chain links wrapped around the cassette. Then again, you need a certain length to get leverage. So aim for 12" to 16" in length.
Take the soaked chain, rinse it off with water from a garden hose, and dry it as best you can with a towel, or paper towels, and by rocking it back and forth through the air.
Next, you'll need to get just a section of that bike chain. In the picture above of my completed chain whip, you'll see it has 55 links. That's a bit long - I'd recommend preparing a length with 36-40 links. That ought to do the trick, even on a 32 tooth cog. Use a chain tool to remove the rivet where you've counted to, and discard the other piece of chain. Or better - if you have an equal or longer length of chain left over, save it for another chain whip for a biking friend! What a Christmas present, eh? Back to the chain tool - if you want to go truly homemade style, use a hacksaw to saw a link in half. You just need to get one side started, then twist to snap that side off. Then repeat on the other side. I locked the chain in a vise to do the cutting, but you should be able to do this by holding one side of the chain at the edge of table or even on the ground. Don't worry if the chain gets dirt on - you can rinse it off if need be. If you cut the chain with a hacksaw, then you should file down the edges a bit. But you don't have to - the thing is, that half link will fold right inside its connecting link, and you can tape off that final link with electrical tape. You can see in the picture, I took a few minutes to file down the sharp edges and didn't tape off that final link.
This step is key. You're about to attach the chain to the piece of wood. It's not hard to do, but one thing needs to be right: the grain of the wood must be oriented correctly. Place the piece of wood on your work area so the grain is visible on the top surface. You must put the screws into the wood where you can see the grain lines - that is, with the grain. If you don't, the bottom screw won't stay in when you try to torque off the cassette lockring. How do I know this? Trial and error! On my first attempt, I screwed into the smooth side of the wood, where no grain shows, and that bottom screw popped right out under load. The chain whip you see in the final picture above shows the smooth edge of the wood, since that's a side shot. The picture at left shows what the grain side of the wood looks like.
Now, screw the top wood screw in about 1" below the top of your wood piece. Count 7 links, then screw in the chain on the 8th link. You want to create a small loop (see picture). How big a loop is technically correct? I'm not sure - it's just a visual thing. Imagine what chain whips you've seen look like, and do your best. You may want 8 links in that loop. Be careful with the bottom wood screw to really center it in the wood, and screw it in as straight as possible. It is this screw that will be bearing all the force you apply to the lockring when you go to remove your cassette.
Lastly, tape the handle. This was a bonus step for me, just so it looked better for the picture! But I suppose you and I might avoid splinters this way, so go ahead and tape it off. Use electrical tape or the ever-reliable duct tape.
Now if anything could go wrong, it would be that bottom wood screw popping out. So on your first use, wear protective eyewear, and make sure the loop part of the chain whip is pointing roughly downward toward the ground.
And that's it! You've just built your own bike chain whip. You will now be the envy of all your biking friends. And like I said before, you now have an instant Christmas gift on the ready!
For more information on bicycle chain whips, see: Chain Whips