How is the conservation of momentum related to Newton's third law?

This answer can be given in a very short answer.

The third law of newton states that for every reaction there is an equal and opposite reaction. The states that the combined mass times velocity or momentum of two objects should remain the same if not affected by outside forces. Therefore if one fast object hits another stationary object (neglect air resistance and other outside forces) then the other will gain momentum and the first will lose momentum but the combined momentum of the two objects will be the same as before they interacted. Therefore you get the equal reaction that newton talked about.