First of all it is very rarely used, for it is there mainly for serious criminal acts against an individual or Vulcan as a whole (Serious Criminal Act 1 - SCA1). Such crimes are extremely rare - maybe one in 100 earth years.
Crimes agains the Federation (CF02), are dealt with by the Federation representative on Vulcan - these crimes, too, are rare.
Petty crimes (CC012) are usually dealt with by the individual's clan or the family circle. Such crimes are, however, nearly unheard of and highly illogical, for they are for personal gain.
All other (VMC3001) "crimes": immoral acts, acts agains the Vulcan philosophy and tradition, are dealt with by the family or the individual's teacher (master) in the Vulcan mental techniques.
Here, I shall deal with the SCA1 crimes.
The Vulcan word for crime - tr'aiyar literally means 'an invasive procedure'. Under SCA1 against an individual are listed in order of gravity:
1) Breaking of mind-link between bonded couples - p'pil'lay
2) Mind-rape - Kae'at k'lasa
3) Murder - t'r'vavat
4) Mind-eavesdropping - kae'at knal'lur
5) Grievous bodily harm (no Vulcan word)
agains the state:
1) Treason - kam'nat (this includes a large number of things, including theft against Vulcan-state)
If a Vulcan is seriously suspected of any SCA1 crime, and he/she denies the charge, then a Verification (t'amatar'am) is called for. The suspect is his own witness. In a verification, a group of healers will seek the truth from the suspect's own mind by a mind-meld. Included in this group can be the injured party. An arbiter and guardian of the Law (e.g. T'Pau) is also included to prevent the Verification from straying into areas of privacy that are irrelevant to the investigation.
If the suspect is guilty (or if he/she admits to the crime) then he/she is faced with a number of choices. As every Vulcan believes that any crime is the cause of an unbalanced/ill mind, the main offer is Retraining (mind-techniques) which would be done in pleasant surroundings by a trained healer. The retraining does not mean mind-erasing or adjusting the persons mind - that would be a direct violation of the IDIC principle. The perpetrator is confined in very nice environment (for Vulcans also believe that prisoners should not be punished as the act is usually its own punishment) until the mind-technicians/healers can guarantee that the perpetrator will behave as "sane" Vulcans, permanently. If a person does not, himself or herself come to regret their actions and change their patterns of behaviour away from such, then they stay confined, until they die, if necessary.
The other choice is death, often by the perpetrator stopping his own heart (occures only rarely, as Vulcans value life too much).
Or a Vulcan or a group of Vulcans (If they are not dangerous to others) may choose banishment, so that they can find their own way to peace and logic.
Some information has been obtained from Spock's World by Diane Duane and the Vulcan Academy Murders by J. Lorrah.