The "PizzaGate" rumor was started by Reddit users in the r/The_Donald subreddit, a discussion thread for Donald Trump supporters.
The New York Times investigated and came to the following conclusion:
None of it was true. While [Comet Ping Pong pizzeria owner James]
Alefantis has some prominent Democratic friends in Washington and was
a supporter of Mrs. Clinton, he has never met her, does not sell or
abuse children, and is not being investigated by law enforcement for
any of these claims. He and his 40 employees had unwittingly become
real people caught in the middle of a storm of fake news.
Full article here:
Most of the "evidence" for the conspiracy was fabricated by Reddit and 4Chan users, using a combination of images pulled from social media profiles of emplyees and friends of the owner of Comet Ping Pong. There are also emails mentioning or sent by John Podesta included in the "consipracy evidence". However, I read all of those emails, as did the NY Times investigative team, and they do not constitute "evidence" of anything. You can read them yourself, as they are available on wikileaks:
Snopes notes that child abuse rings are uncommon and that most child abuse is committed by close friends or family:
...while rumors about pedophilia and child trafficking remain standard
in urban folklore, roughly 90 percent [PDF] of assaults on children in
the U.S. are committed by a friend or family member, a number
reiterated by the United States Department of Justice.
In summary, there is no evidence in those emails that supports the conclusions alleged by openly pro-Trump sources. The sources themselves are suspect based on their political allegiance and their past behavior.