While  we often see images of people floating around in the vomit comet (an  airplane that flies a series of parabolas to put the inhabitants into  free fall), we don't really use that method to train astronauts, other  than for familiarization flights when they are astronaut candidates.

Microgravity  training for astronauts is mostly in the context of performing EVA  (spacewalks).  EVA are trained in a vast swimming pool called the NBL  (Neutral Buoyancy Laboratory).  The astronauts are put into spacesuits  and then lowered into that pool.  Within the pool are life size mockups  of parts of the space station.

 The  buoyancy of the water feels similar to microgravity.  The astronauts  have to get used to the tendency to float away from the work location.   Tools float away.  They say it is a pretty accurate simulation.