How do you make a melee attack?
I can confirm it's the right trigger. I just checked on my Xbox 360. It's really a last-ditch sort of thing; I wouldn't suggest counting on it.
It is the right trigger, but more importantly you need to make sure you are not also holding down the left trigger or you will fire the weapon instead of initiating a melee attack.
I believe the right trigger is the melee attack with whatever you're holding.