Judging by Vera Farmiga’s revelation to Metro, it’s a good bet that Dr. Emma Russell is working for Monarch, and through trial and error has devised a way to talk with the monsters.
From there, she can potentially control their actions.
Given the destruction Godzilla and these other monsters have wreaked, you can’t blame humanity for creating a meands to get them under control, but it isn’t a stretch to assume that something will go wrong with this science.
It’s unclear how much time has passed since the events of Godzilla when Godzilla: King of the Monsters starts, but given that the former movie marked the public’s exposure to these monsters (the “incident” in Kong: Skull Island was most definitely kept under wraps), no doubt that Earth’s greatest minds from both Monarch and other organizations haven been wracking their brains on how to deal with these creatures.