Most second storey noise is impact noise on the floorboards, people walking, furniture shifting, chairs etc.
If is is just impact noise - you can roll cork or felt underlay over the entire floor area (similar to that used in floating floors) then put your carpet underlay over that, carpet on top and that should be that.
If your problem is conversation, or music being carried through, this is usually casued by vibration in the air rather than direct transfer through the structure. The previous posts with insulation between the joists will help alleviate this, though depending on the severity of noise a multi layer effect of felt, underlay and carpet will deal with most domestic situations.