I strongly suspect that one or more of the diodes inside the alternator
failed shorted and the alternator needs replacing.

Sorry in advance for boring you with some details :)
In simple terms, think of diodes as one way valves when it comes to current:
they allow current to only flow in one direction. On alternators, diodes
"make" DC from the AC that the alternator generates. When boosting, they
also make sure that the current being supplied by the booster cables is not
allowed to flow through the alternator as it isn't designed to do that.
On your alternator,  the shorted (bad) diodes conduct in both directions so
current from the booster cables is not stopped, causing current to go
through it when boosting. This is a lot more current than the alternator can
handle so it smokes - it may have damaged more than the diodes now.

Try to get the car running again and measure the voltage across the battery
while running. You can buy a cheap multimeter at radio shack or sears(if you
are in the US), if you don't have one. Make sure you understand how to read
DC voltage before you use it.
It should be about 14.5 volts DC (the normal charging voltage).
If you don't see 14.5V DC, you could switch to AC out of curiousity and most
likely measure several volts AC, indicating that the diodes are blown. If
you don't see a charging voltage, I'd replace the alternator. On some
Honda/Accura alternators one can just put new diodes in, so it may pay to
check with the dealer on the replacement parts.

If anything else, just report  back here.
Remco