The cochlea is the inner part of the ear responsible for most hearing. Tinnitus is generally thought to be caused by neurons firing sporadically due to hearing loss. It occurs in quiet environments, because any quiet noise will be too low to hear, and instead, the nerve damage will cause ringing. There was somewhat recently (2001) a study on whether cochlear implants help with tinnitus. This study showed that by restoring the cochlea with an implant, tinnitus is reduced or removed completely.

The brain probably knows to stop the ringing because it can again hear what actual quiet sounds are happening, and therefore there is no random neuron firing. Really good question.