Dig a hole that is 3 inches wider and 3 inches deeper than the bucket. This is for the water basin for the waterfall.
Place a 2-inch layer of gravel in the bottom of the hole for the bucket. Spread a 1-inch layer of sand on top of the gravel. Place the bucket in the center of the hole. Fill the space between the bucket and the hole with tightly packed sand.
Fill the water basin with water to about 3 inches below the rim. Place the pond pump inside the bucket. Pull the pond pump's electrical cord and the water delivery tube outside of the bucket.
Cut a piece of rock screen 1 foot larger than the water bucket and place it on top of the bucket. Stack large stones all around the bucket to hold the screen in place and disguise the electrical cord and water pump.
Stack large stones to form a waterfall on one side of the bucket. Do not make the waterfall any wider than the bucket. Continually dump a cup of water down the waterfall rocks to be sure the water will flow into the basin. Add stones until waterfall is the desired size.
Thread the end of the water delivery tube through the stones in the waterfall so it sits at the top of it. Cover the ground around the waterfall with small pebbles. Put small pebbles on top of the rock screen to hide the water basin. Connect the water pump to an electrical source. Adjust the water delivery tube if needed to get the water flowing properly.