I had two suspected infected after a wereskink attack, so I put them in a side room. Only one turned out to be infected, and is currently devouring the other dwarf.
Easiest way to deal with this is to put the suspected werebeasts in the military and station them on the corners of the map, out of sight of the others. You can do this 1-2 days before the full moon (but just keep an eye on them to see if they do something stupid like go to get a drink). If they can't see anything to attack, they will just stand there.
Now that you have a werebeast, if you want to keep them alive, you just need to remember to station them somewhere secluded every month (warning: the full moon shifts by 2 days every month!). I built a small hut (without a door!) for mine so he didn't get rained on. You should also give them a flask/waterskin so that they always have a drink, which will reduce the occurrences of them wandering off to get a drink right at the full moon. Also, if you get seiged, werebeast is out the door, obviously since you can't reasonably open up all the gates at full moon.
Basically, as long a nobody sees the transformed dwarf, you will be a-OK. If you make a mistake, and a dwarf starts attacking/being attacked, do *not* attempt to save them. Burrow your guys out of sight. If anyone witnesses the attack, it can cause a loyalty cascade which can take out half your fortress.
I notice many people being frustrated with werebeasts, but while fiddly, they are not that hard to manage.