Basically, they tell them. Short of the weapon transforming, they really don't know when they're human who's a weapon and who's a meister. xD Later on you see a flashback of like the first day of school, apparently they all wear little nametags saying either Weapon or Meister and find partners that way.
I can't help but think that would be a terrible school for me, I can't even pick partners in normal classes. XD;
Told you that the weapons are people :P and omg the cat girl is so cute. The only thing that really annoys me about the show is that they don't delve into the different magical things that exist. Like, they introduce cat girl, they let you know that there are other cat girls, but that's it. And they introduce a zombie once, and never introduce any other zombies or make it seem like a big deal. Then there are witches that turn into animals, but they're not the same as the cat girls that turn into animals...idgi xD