My system is not perfect--none is--but the number of chess pieces lost from a dozen chess sets and many hundreds of young hands has been minimal. I teach second graders and other young players to put chess pieces in the bag according to the "rule of four". Start with the royalty: two queens and two kings, four pieces. Then, four bishops (the clergy). Four cavalry (knights). Four chariots (the original name for the rook). Then, four pawns, four pawns, four pawns, and four more pawns.
If at any point four pieces are not easily found, check the floor.
I put away my own chess sets by the same method.