You will need a long dowel (4' is good and easy to find at my local hardware store, but if you're as tall as I am a little longer would be convenient) about 1.5" in diameter, a shorter dowel about 1" diameter (I like 18", which I get by buying a 3-footer and cutting it in half), a box of roofing nails, and a bunch of bottle caps. The most traditional approach, and the origin of the instrument's name, is to save the bottle caps from beer, but you can also get unused ones from your local homebrew store. Or some of both - you're gonna need a bunch of them. (I used 144 for the one illustrated here.)
Step 1: Cut the Rattler Stick
Step 2: Drill the Pilot Holes
How you lay these holes out on the dowel does not matter. Straight even lines of them up two or four sides of the dowel is a common choice; for the one shown here I took a cue from nature and had them spiraling up around the sides with five spirals going one way and eight the other. Just make sure there's enough clearance that all holes are at least slightly wider than 3/4" apart, since that's the diameter of a beer bottle cap and you want room for them to rattle around.
Step 3: Pierce the Bottle Caps
(A safety note - my fingers are approaching the cap in the picture to take it off the drill bit, but keep them well away while the drill is spinning. The cap can and sometimes will slip on the plywood, so you don't want fingers even remotely close to the drill bit.)
Step 4: Assemble the Lagerphone
When you're doing this, you want it to still stick out a fair amount; the goal is to leave plenty of room for the bottle caps to rattle around, rather than nailing them firmly into place.
Step 5: Play!
There are several things you can do to play it. First, you can hold the body of the instrument off the ground and swish it around, making the bottle caps rattle as loudly as they care to. Next, you can pound it on the ground firmly. You can also hit it with the rattler stick while it's planted on the ground; the sound of wood striking wood will be complemented by a softer cap-rattling sound. You can also take the notched side of the rattler stick, press it firmly against the main part of the instrument, and draw it across the body of the dowel, making it rattle back and forth for a washboard-like sound. This can be done with the long dowel either on the ground or off; when it's off the ground, the caps shake around more and make a little more noise.
These techniques give you a fairly broad selection of effects it can produce, from such a simple instrument, but of course anything else you can think of is fine as well - it's a very sturdy instrument and you shouldn't be afraid of hurting it if you experiment. It sounds best when you have a guitarist or other stringed instrument playing with you, since normally this is the rhythm section in an Australian folk ensemble. (The Aussies got it from similar things being used in 19th-century England, so it'll fit right in with English or American folk tunes as well.)