BHS -> Mr. Stanbrough -> Physics -> Mechanics -> Momentum -> this page
It's very simple, actually. Newton's Laws (particularly the Third Law) guarantee that every interaction involves exactly two particles (A pushes B, B pushes A) and we have already established that momentum will always be conserved in every two-particle interaction. That's all there is to it! Even if there are uncountable billions of particles in a system, every interaction can be broken down into two-particle interactions, and momentum is conserved in every one of them. Therefore, momentum must be conserved in every isolated system - no matter what it contains.