Zero-gravity combat training or null-gravity combat exercises were a part of standard Starfleet Academy training.
Malcolm Reed experienced an unfortunate condition during his zero g training in the EV simulator at Lunaport which was also called "the Vomitorium" by Starfleet trainees. Phlox later told him that this was noted in his medical file. (ENT: "The Catwalk")
They later employed some of their null-gravity combat training during the expedition to combat Tchar, after he activated a gravity neutralizer in the Skorr temple, forcing those on the expedition to "fly and fight as a Skorr." (TAS: "The Jihad")
In 2373/2063, when the crew of the USS Enterprise-E found out that that the Borg that had infested the ship were outside on the hull building an interplexing beacon on the ship's deflector dish, Captain Jean-Luc Picard asked Lieutenant Commander Worf if he had remembered his zero-g combat training. Worf revealed it made him sick to his stomach. Despite this, Picard, Worf and Hawk went onto the hull to stop the Borg. (Star Trek: First Contact)