How can you make a successful egg drop container?

You would have to account for all the places that might hit the egg and all the forces that act on it.

You should have a parachute-like structure to create drag/air resistance to slow its fall. You should make the bottom of the container that holds the egg soft (eg. with a sponge). You should cover the container with a soft material such that if it were to rotate upside-down, it would fall on something soft. Make sure the egg is not moving freely in the container. Put fillings (eg. Bubble Wrap) around the egg such that it does not move freely when it falls and hits the ground.

It should be very similar to the boxes that come when you buy electronics, except for the fact that it would be smaller and would have a parachute.

Good Luck.