The actor spoke with PEOPLE at CinemaCon in Las Vegas on Tuesday before the whole cast appeared before a collection of movie theater owners. Jared Leto, he said, wasn't messing around when it came to his diabolical character.
"Jared really set it off because he was sort of sequestered away from the rest of us," Smith said. "He was off in another world in his preparation. We were bonding and we were working together and then we got our first glimpse of the work Jared was doing."
Smith said Leto sent the rest of the actors a video in full character – this was before "The Joker" sent a live rat to costar Margot Robbie; before he sent bullets to Will Smith; before he sent used condoms to Adewale Akinnuoye-Agbaje, who plays Killer Croc.
"We were like, 'Wow, Jared is taking this [expletive] really seriously,' " Smith said of the video. "We really need to get it together. Jared really set the tone for everybody to step up to."
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Akinnuoye-Agbaje told PEOPLE at the event that Leto's antics helped the rest of the cast form a tighter bond. "What was great was it really created the atmosphere of us against them, and it united us against them because we had a common enemy, which was now the Joker," he said.
"If I tell you some of the stuff he sent me, you'd be like, 'What is in this guys mind?' " he added of Leto's special gifts. "I got used condoms, I got all kinds of stuff and I was like, this is no longer a joke, this is personal."
Robbie also talked about Leto's shenanigans, although she was a bit hesitant to go into detail. "The craziest ones I can't actually talk about," she said. "Everyone was up to no good on this shoot. It was a long shoot. People were enjoying themselves."
For Smith to play his diabolical Deadshot character for the film, it took some time to even attempt to understand why this man was so vile.
"With this character, I couldn't get my head around how you can just kill someday and go take your daughter Christmas shopping," he said, "so that was a really strange kind of physiological pursuit for me, so I started studying serial killers."
He said he read a book that begins with a line: "Everything that everybody does is cause it feels good."
"So the question isn't why do they do it, the question is why did it feel good?" Smith said. "That really opened up Deadshot for me. Why did it feel good to kill people?"