What is best way to add support to a dresser drawer?

You might be able to replace those sagging bottoms. You will have to look carefully at the bottom of your drawer and see if there is a slot that the bottoms slide into. If so you may be able to take the back part of the drawer off and slide old wood out/new wood in. You will have to get the same thickness of wood and have the tools to cut the sizes you need. Plywood comes in different thicknesses. I have done this numerous times and it works well.

If the bottom plywood is warped, it will always bind. Replace the bottom. You can notch out the wood support in the center of the front and back of the dresser to add a 1" x 1/2" wood runner for it to glide over (wax or soap the runner). Must be level with the original wood at front and back.

Have you tried reversing the warped drawers? You could dampen them with the spray bottle of water and then just get them back in with a book or some heavy weight or just out clothing back in after it's dried. Also staple the bottom drawer to the back and sides Of dresser drawer. Check first to see how it was put together.

Mine was just lightly stapled but I was able to repair it by reversing the bottom part, and re-inforcing existing staples ( or small nails)

hope this is helpful

I agree with Gk. Replace the bottom. Usually stapled to the back of the drawer and slides right out. I have used thin plywood or hardboard for drawer bottoms. Hardboard doesn't warp as much.