The build-up to Arya's murder of Ser Meryn Trant is pretty intense, but the actual murder itself is over in a matter of seconds. As you'll recall, Arya puts the cowardly former knight of the Kingsguard on her list for killing her sword-fighting instructor, Syrio Forel, in season one. The Lannisters had sent Trant to apprehend Arya as part of their plan to have Joffrey ascend the Iron Throne, but the Braavosi defends Arya and disarms the guards with just a wooden practice sword (prompting fury and disbelief from Trant). Trant then draws his own sword and battles Syrio, as Arya obeys her instructor's warning to flee.
But anyway — back to his gruesome death! In season five, Arya spots Trant in Braavos when he visits the city as an escort of Mace Tyrell. Knowing his sick preference for very, very young girls, Arya sneaks into a brothel that Trant is patronizing and disguises herself as one of three girls he wants to spend the night with. He beats them, and only Arya remains stoic, which pisses him off.
When he sends the other two away so he can continue brutalizing her, she rips the face off to show him who she really is, and then stabs him multiple times in the eyes and chest. In a calm, almost monotone voice, she tells Trant that she is Arya Stark and this is for the murder of Syrio. Then she slits his throat, as she is wont to do.