My Beetle's handbrake doesn't click and stay on. The button on the handle also comes out (with the long stiff wire with a half-loop on the end). So I think it's come "undone" at the clicker/ratchet mechanism. Here is a pic of a round-end bit of metal haning loose under the handle... how do I fix it?

Kind of hard to explain but that half loop in the wire needs to fit around that round ended bit of metal there.
You need to pull up on the handbrake until the round ended bit of metal clears the ratchet so you can spin it around.
When the round ended end of the metal peice is up inside the handbrake lever the half loop in the wire needs to be put over it. then just press in the button and lower the lever.

thats correct Chewy...

I believe it only happens [to me at least] when the handbrake needs adjusting....

If You don't have any more thread to adjust the stretched handbrake cables place a larger size nut or a few flat washers under the nut.......
that will keep You going until You replace the brake cables....

Lee

http://community.webshots.com/user/vw68autobug 

once you have it back together again adjust your brakes and make sure your hand brak come on with only 3 of 4 clicks.

What has happened is caused by pulling the hand brake too far up before the brake takes hold.

If you adjust the brakes correctly and it is still to much pull then it is in the cable. There is some adjustment there

Here is a diagram of the handbrake....

The hand brake should only need a few clicks to have the brakes ON.... too much....
due to - brake linings worn too much or cables have stretched.....

As someone said adjust the rear brakes first then do the hand brake.....

I hope this helps...

Lee
http://community.webshots.com/user/vw68autobug 

That all makes good sense, thanks guys! I should be able to fix it now