Everyone has seen videos of the astronauts on board the International Space Station floating around, watching their food fly through the air and otherwise enjoying the zero gravity. The first thing to know is that zero gravity is a misleading term. Gravity on earth keeps us from floating away. Some people think there is no gravity in space, but the laws of physics show that there is. Gravity keeps the moon from crashing into the earth the other planets in their orbits. What's happening on the ISS is the physics of opposite forces. The pull of gravity from the earth is opposite of the gravity forces of the orbital motion of the ISS. They cancel each other out and you have weightlessness. Water droplets from the wash cloth that Commander Hadfield is wringing out in this video don't land on the floor because the ISS motion negates the pull of gravity.
In space, satellites, including the ISS are moving at tremendous horizontal speed. There is no anchored structure to exert any other physical force on them. As they move around in an orbit, the Earth's gravity is still acting on them but it is overcome by their speed. That's why things on board the ISS float, there is an absence not of gravity, but of other external forces that are greater than those on the ISS. All of these complex physics concepts make for a lot of fun for the astronauts, and a cool video that demonstrates the physical forces that keep us in motion on Earth and in space.