First, the report system does its work. Previously, it took being reported in 12-25% of games to trigger a case.
Once a case is built, it's reviewed. Things to look for when reviewing for feeding:
- Build - particularly one focusing on movespeed
- Summoner Spells - Tele/Revive is common for intentional feeders
- KDA - while not the strongest indicator, it can still be a useful marker
- time/locations of deaths - the old Tribunal couldn't tell this, but the new Match History can demonstrate it with a combination of the heat map and timeline.
Keep in mind, this list only covers data that has been offered to players. Lyte has commented that they can actually view a detailed analysis of a game, which shows what each player is actually doing every few seconds.
If, by the reviewer's judgement, the player is intentionally feeding, a sanction is issued. Most commonly (with the Tribunal down) this comes in the form of a 2-week ban. If, by the reviewer's judgement, the player is not intentionally feeding (nor engaging in other forms of toxic behavior), the case is dropped, and nothing further happens.
There may be other steps in between, and things that we as players don't know about, but this should be a fairly decent summary of the process.