When Mordecai hears about this evil plot, he reacts the way any decent Biblical character would react: he puts on sackcloth and ashes and walks around the city, wailing, before finally winding up at the King's gate. Meanwhile, all the other Jews are similarly lamenting over the fate that's been prepared for them.
Esther doesn't know about the impending genocide at first, so she tries to send Mordecai some regular clothes. But he refuses—the sackcloth is a more effective look.
So, she sends the eunuch Hathach to go to Mordecai and ask him what's going on. Mordecai fills him in on Haman's genocidal scheme and the amount of plunder Haman says he wants to put into the king's treasuries. Mordecai shows Hathach a copy of the decree to prove it and asks him to try to get Esther to help prevent the genocide.
A Slightly Reluctant Heroine
Hathach returns to Esther and tells her what Mordecai wants her to do. However, Esther sends a message back to Mordecai, saying that anyone who enters the king's court without permission will be put to death (unless the king excuses them). And the king hasn't asked to see her in about a month.
Mordecai sends back another message, saying that she shouldn't imagine that she can escape this genocide just by hiding out in the castle. Her identity will probably be discovered and she and her father's family will get destroyed, while help comes to the Jews from elsewhere. He suggests that to help prevent the genocide might be the reason she was made queen in the first place.
So, Esther agrees to help—but she says that Mordecai and the other Jews need to help her by fasting for three days. She and her maids will fast as well and see if it all works out. Mordecai goes and organizes this mass fast.