Install thick carpeting or even rugs on the floors causing the noise problem. Thick or heavy carpets can dampen the sound of footsteps by lessening the impact sound vibrations. When installing the carpet, use a heavy-duty carpet pad to provide extra sound protection.
Add additional soft textiles and fabrics to the rooms you would like to keep quiet. Add curtains, tablecloths and additional area rugs to the rooms to reduce the amount of hard space. Hard spaces allow sound waves to vibrate and echo; soft cloths will lessen this effect.
Use mass loaded vinyl barriers under your carpets if you live in an older home. You can install these barriers underneath the carpet or carpet padding. You can even install this material under floating floors. Mass loaded vinyl barriers are strong and wear resistant, and these barriers reduce sound by slowing noise transfer.
Use a constrained layer damping (CLD) component to install a second ceiling in the room you wish to soundproof. Apply up to two tubes of a CLD product to individual sheets of 4-by-8-foot drywall. Attach the CLD-treated drywall to the pre-existing ceiling. The addition of the a CLD compound and new drywall adds to the insulation of the room.
Check your ceiling for any gaps or holes. Airspaces between the ceiling and the floor can allow sound to travel down to the lower level; fill these holes with caulking material.