Choose a large decorative tray that's wide enough to hold your necklaces length-wise. Lay them out in a row in the tray, organizing by color or style as you go. The tray doesn't need to be made for jewelry. Try using a vintage serving tray, for instance. No matter where you buy jewelry, you often end up with small cardboard boxes. Use paperclips to attach them together. Set 2 bottoms side-by-side, and put the paperclip over the joined edges. Lay the boxes out in shallow drawer or tray. Place a necklace in each jewelry box. It's fine to let costume jewelry be out in the open, but you should protect more expensive jewelry from dust and damage. Place each necklace in its own jewelry box, and put the boxes away for safe keeping. You can also use jewelry boxes that have individual spaces for necklaces. Many of these are decorative and will look lovely sitting on a dresser or vanity.
Pick a decorative tray for an easy way to lay out necklaces. Organize necklaces in the cardboard boxes the jewelry came in. Hide more expensive pieces in individual jewelry boxes.