Measure the dimensions of the inside of the drawer with measuring tape or a tape measure.. Due to its pliability, a soft measuring tape as commonly used for sewing may be best.
Cut a false drawer bottom using the plywood sheet. Use the dimensions of the inside of the drawer as a guide, making both the length and width 1/8-inch smaller than the guide.
Measure the necessary height based on objects you intend to hide. For the purposes of subtlety, it is a good idea to not have your false bottom be much more than 1 inch above the drawer's actual bottom. Mark the inside of the drawer where the false bottom will sit.
Insert screws into the drawer's side, at the height marked. All should be at the same height, to ensure that the false bottom sits naturally. Four screws will be necessary: two on either side, in the front and back of the drawer.
Insert your secret possessions into the space underneath the screws in the drawer, and then place the false bottom on top.