How do I make a boss with multiple forms?

It's simple really. Go into the enemy editor and make enemies for each of the boss's forms. Now go to the enemy you're using as the first form, go to "Spawning" and enter

Spawn on death: (Form2)

where Form2 is the name of the enemy you are using as the second form. Then, if there's more forms, go to the second one, and set its spawning to the third form, and so forth.

However, there's one more step. When an enemy "spawns on death", it will take the first available "enemy slot" in battle. However, the first form will still be dying when the second is spawned, so you should go into the Formation Editor, and place the second slot at the same spot the first form is (add an enemy, position it, then remove it). Third (and after) forms are already ok, since the first slot (should) be empty by the time they get spawned.

See HOWTO Chapter Bosses for more on multiple forms.