Cut a straw down one side with a box cutter or craft knife to create one long slit. Thread one side of the necklace through the slit so that side of the necklace is held in place by the straw. The straw will help keep the necklace from tangling with other necklaces.  Lay the necklaces out flat in the drawer. Line the bottom of the drawer with a piece of velvet to keep the necklaces from sliding around. Fasten the ends shut so the strands aren't loose. Find trays with long slots in them that you can lay in the drawers. Your necklaces can go in the trays, keeping them safe and organized. You can even use plastic silverware dividers for this purpose. Spice jars usually have just enough space to fit a single necklace. Put one necklace in each jar, and place them in your drawer. Place a non-skid surface underneath to keep the jars from sliding around.  Some spice jars are magnetic, so if you prefer, you can use the magnets to attach them to a mirror or metal surface instead of putting them in the drawer. Stick to beaded necklaces, as delicate necklaces might get tangled up in the jars. Grab an old teacup from your kitchen, and place your everyday necklaces in it. Alternatively, if you have a deeper drawer with extra space, you can line multiple teacups up in the drawer. Place a necklace in each cup to keep them organized.
Separate necklaces with plastic straws for a cheap organizer. Add inserts specifically for jewelry for an easy solution. Organize your beaded necklaces with spice jars. Place your most used necklaces in a teacup on your dresser.