Here's how the system operates: when a content owner -- say, a movie studio -- detects that its work is being shared on a peer-to-peer network, it makes a note of the IP address that's sharing the file and contacts the ISP that services that address. The ISP then notifies the user with that IP address about the apparent copyright infringement. "Initial alerts are merely educational, letting the user know that unauthorized content sharing was detected on their Internet account," explains the Center for Copyright Information in a video.
Repeated infringement, though, will cause you to run afoul of two "additional alert levels." The first, the CCI says, is "acknowledgement": a user has to fill out a form stating that they've received repeated notices of copyright infringement. The second step is the ominously-named "mitigation," in which the user's ISP reduces the account's connection speed or takes other slightly-punitive measures. (Strangely, the CCI offers "watch[ing] an educational video" as an appropriate alternative to performing both steps.) Customers who have been wrongly accused can appeal the mitigation step, though submitting an appeal costs $35.