Proof #1, Universal gravitation:
all matter in the universe is attracted to all other matter in the universe. This is gravity.
When matter is held together, the gravity wells together, and focusses in the center. Because matter is drawing towards the center of the gravity well, the surface tends to form a curve equidistant to the center.
However, there are bumps, mountains, valleys and trenches, so the globe is lumpy, but it DOES follow the shape of a globe.
Proof #2 The horizon.
Stand on a beach, and watch a boat sail away. The boat appears to travel DOWNWARD over the horizon. It does so because it is moving along the curve of the earth.
Proof #3 The view from an aeroplane:
In an aeroplane, the curve of the earth is clearly visible.
Proof #4. Converging paths:
If you travel East from Asia, you arrive at the Americas.
If you travel West from Europe, you arrive at the Americas.
If you travel North from Russia, and keep traveling in a straight line, you will find yourself traveling Southward over Canada.
This happening necessitates the Earth being round.
Proof #5 Satellite imagery:
We have satellite images of a round Earth.
Proof #6 The ridiculous proof:
If the Earth were flat, the sun would extinguish itself in the ocean.