The CS:GO team wrote in their announcement:

"Because the new system is driven by reports, it lets players establish their own standards for communication and ensure that their fellow players receive anonymous feedback when they're out of line."

While they didn't reveal how many reports a user has to get before they issue a warning, the team clarified that reports from those who play frequently and don't report often carry more weight, most likely as an effort to prevent people from gaming the system. Meanwhile, accounts "that generate no XP and/or spam reports will have little to no impact." It's still unclear when they'll start sending out warnings, but they said they've already started tracking players' reports with the new system. They're also encouraging players to report toxic players for "Abusive Communications or Profile."