I was trying to tap a hole in aluminum with a 1/4" tap. Half of the tap broke off in the workpiece. How do I get it out?

Ideally you would want to use a tap extractor. These are readily available from catalog houses such as Grainger and McMaster-Carr. If you do not have access or the time you may try the following. The smaller size makes it more difficult. First, see if you can find a couple of small nails that will fit into the flute or groove of the broken tap. Insert them into two grooves or flutes across from each other. Clamp onto them with a pair of locking pliers. Try to turn the piece out with the nails. If the piece is broken off flush with the top of the hole you may try to turn the piece by striking it with a punch. This may be more successful if two people can punch it at the same time.