I periodically post this, but were attacks are not so difficult if you are well prepared.
First: Don't panic! The full moon lasts for only a few days (2-3). The were creature may not have appeared on the map at the exact start of the full moon. So the best way to survive is simply to wait until the full moon finishes and they turn back. Then send the militia after them so that they can't come back another day.
Second: Burrow everybody. Were creatures are building destroyers and trap avoid. They will spend their time destroying buildings if you have buildings to destroy. If the were creature can not see anyone, they will not move. This is super important to understand. No creatures in line of sight (and no buildings to destroy) == completely harmless were creature.
Third: The earlier you discover the were creature, the more time you have to burrow. Tie up some dogs around the site. As a bonus, the were creature will run up to the dogs and kill them -- taking precious time out of their full-moon-counter. The more time they spend killing your dogs, the less time they have to kill your dwarfs. Dogs will not become were-dogs.
Fourth: If your dwarfs do not make it back to the burrow, they are already dead. Do not try to rescue them. Do no try to engage the were beast with your militia (unless you have full metal armour cover -- and even then, there is not reason to risk it). Your dwarfs will buy precious time for the rest of the fortress.
Fifth: If your dwarf gets bitten and survives, then on the full moon, station them somewhere where they can't see any creatures. You can find the next full moon by looking at the wiki, or by looking at the moon icon on the edge of the screen. Try to station them a couple days ahead because they might decided to go get a drink, or pray, or whatever. As long as the were dwarf is stationed somewhere where they can't see a creature and can't see a building to destroy, they will not move at all. You can station individual dwarfs from the squad menu (they have to be a member of the squad). You can have as many were creatures in your fortress as you want *with no danger* as long as you station them somewhere secluded during the full moon.
Sixth: If your were dwarf accidentally sees another dwarf (because a kitten wanders over to them and then runs back into the fortress :-P), lock down the area. Anybody who sees the conflict is at risk of getting into a loyalty cascade. If a loyalty cascade happens (your dwarfs start killing each other), they are already dead. Do *not* attempt to rescue them. Lock them in and wait until the fighting stops (usually when one side wins -- often a single dwarf).