Basically, drill and tap a hole for a machine screw. Glue and screw the parts together. Done. You don't have to use a 6-32 machine screw. That's just what I had in the house.
Took me about 2 hours, but I made several mistakes. You can avoid those mistakes by looking through these instructions. I think it's about an hour of work if you have the tools and do it right the first time.
You'll need a bunch of tools. If you don't already have a drill press, drill bits suitable for metal, a hack saw, file, screw drivers, etc, this will be a very expensive project. If you're without tools or experience, you should seriously consider asking your friend to do it for you.
You could just buy the replacement part, but you'll still have to take the tripod apart. The replacement part doesn't come itself; it comes packaged with the upper leg part. Also, you'll have to figure out the vintage of your tripod. Bogen has been making this model for years and there are subtle differences. (If you do buy a new part, at least recycle the broken bit.) And these are just the practical difficulties.
The reason I chose not to buy the replacement that I'm philosophically opposed to thinking of everything as disposable. Disposable items make sense for certain applications---medical supplies, for example. But do we really need to have something disposable to wipe off the kitchen counter? Or eat off of?
Repairing the stuff you already have is green because it reduces the amount of stuff in landfills and promotes responsible thinking. (It's better than recycling because recycling is often promoted by plastic-producing companies---to dull the guilt of buying plastic stuff. Also, it's harder than you'd think to recycle plastic. And the environmental impact of the transportation involved in curb-side recycling programs may offset whatever small advantage there is to recycling glass.)
Step 1: Disassemble and Drill
Now, epoxy the broken parts together and drill a hole. Make sure you use the right size drill bit. The upper hole should allow a 6-32 machine screw to pass through and the lower hole should be the right size for tapping threads.
Drilling one size hole through the whole thing is not a good idea because then the threads must match perfectly between the two parts. It's very likely that the parts will come apart while trying to cut threads, so I wouldn't advise it.
The depth of the hole should be enough the accommodate at least 1 cm of the machine screw. Unless you have a blind tap kit, you'll need another 5-10 mm for the tap. It's tapered, which means there won't be threads quite to the end of the tap.
Step 2: Cut Threads
The idea here is to let the small broken bit move freely on the machine screw so that it can be tightened down the the main part of the casting without a gap forming between due to thread misalignment.
It's best to not break the tap.
You can get the threads cut pretty will by hand. I've never had trouble getting the tap centered and level enough. That said, larger projects that involve harder metals may require a little more care. But for this project, you should be able to cut good enough threads without problems.
If you feel resistance (or see the tap flexing) you can back the tap out and get rid of some of the metal chips. Then go back at it. Firm pressure is needed in some cases, but caution is better than putting a project on hold until the hardware store is open the next morning.
Use a bit of light oil on the tap, if you have any.
Step 3: Assemble and Tune
The head of the machine screw will be in the way, so another modification is needed. If the screw has a pan-type head, file down a place to accommodate the head of the machine screw. Make it as perpendicular to the screw axis as possible. Other types of heads can be accommodated with counter-sunk or counter-bored holes.
Put some epoxy on the faces and in the threads (female side) and assemble the parts. Tighten the machine screw and let the glue set.
Step 4: Feel Terribly Clever
Re-Assemble the tripod and go take some pictures with it.