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How is weightlessness simulated?
Short answer
On Earth, weightlessness can only be reproduced temporarily or partially. Genuine free fall is provided by parabolic flights, with about 20 seconds per parabola, and drop towers, with just a few seconds. For spacewalks, astronauts train in large pools, and for physical effects, weeks-long bed rest studies are used.

Weightlessness cannot be generated on Earth, only reproduced: either through genuine free fall for a short time, or through methods that mimic some of its effects.
Brief free fall
The closest match is the parabolic flight. A modified commercial aircraft climbs at a steep angle and then follows a parabolic trajectory; for about 20 seconds everything on board floats. Before and after each parabola, a phase of roughly 1.8 g pushes the occupants against the floor. Dozens of parabolas per flight provide enough measurement time, although each experiment has to be split into small fragments.
Drop towers are even cleaner, though briefer: in an airless tube, an experiment capsule falls for a few seconds with no disturbance at all, because air resistance disappears too. Sounding rockets provide a few minutes of microgravity, though without a crew.
Water instead of free fall
To train for spacewalks, space agencies use large immersion pools. The suit and tools are balanced with weights and floats so they neither rise nor sink in the water. It isn't real floating: the water slows down any movement, the body still senses which way is up, and the suit presses differently than it would in a vacuum. Even so, it's enough to practise manoeuvres, procedures and anchor points on a full-scale replica of the station.
Simulation for the body
When it comes to physiology, less is enough: volunteers spend weeks in a bed tilted slightly head-down, which reproduces, in a way similar to orbit, the shift of fluids and the loss of muscle and bone mass. To practise movements in lunar gravity, astronauts are suspended in pulley systems that remove part of their weight. Virtual reality complements these methods when it comes to orientation and procedures in space.
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