Best Option: Using Rubber Underlayment
Solid rubber is the most efficient soundproof underlay for isolation of airborne and floor noise reduction. The thickness of the rubber needed for your project will vary depending on performance requirements, type of sub-floor, and the resilience of the ceiling below. Read Maximizing Rubber Underlayment Performance for more information.
Second Option: Dampen the Floors
Over wood structures, adding layers of mass with a damping compound between will help to isolate both airborne and footfall impact noise transfer. If the ceilings below are resilient, the benefit of adding a damping compound to the floor will be increased dramatically.
Third Option: Add An Acoustically Dead Material to the Floors
Simple wood structures with minimal mass can benefit from the addition of TotalMass Barrier MLV. Somewhat by the additional mass, but mostly by adding a material to the assembly that does not resonate like other common building materials. Only gains in airborne isolation can be expected.