Dig around each placed stone with the blade of a garden spade to loosen the turf and dirt. Place each stone over to one side so that you can remove the loosened dirt and grass.
Dig out the turf and soil to a depth of approximately 7.5 inches -- more or less. The actual depth you should dig will depend on the depth of each stepping stone. The thicker the stone, the deeper you will need to dig. The top of each stone will ultimately need to be level with the ground surrounding it. Dig each hole approximately 1 inch deeper than it needs to be so that you can add filler to the hole for stabilizing purposes.
Pour an even layer of coarse sand into the bottom of each hole. Place each stone on top of the sand in each hole and wiggle it around to level it. The top of the stone should be level with the ground surrounding it. If it's not, remove the stone and add more sand before replacing it.
Fill in the rest of the hole with sand to stabilize the stone so it won't move. Water each hole to set the sand.