In the film Deep Impact the scenes where all the astronauts are inside the messiah spaceship seemed fairly realistic with gravity e.g. they moved slowly and floating etc.
How did they film the scenes within the spacecraft cabin?
I don't know how good their source is, but the website VFXHQ says the effect was done by hanging people and objects from wires and then removing the wires in post-production.
Zero gravity in the Messiah was accomplished by hanging the actors and props on wires, wires which then need to be painstakingly removed. Amidst all the great 2D work, one wire removal apparently went awry--look carefully as a Messiah crewmember tows a piece of equipment across the ship.
That article doesn't explain how wires are removed from the final images, but there are various techniques which involve in some way "painting over" the wires. This article describes various techniques: