The below information was taken from GMs' forum posts.

To successfully accuse:
Target does NOT have to be a Necromancer.
Target must be in a justice zone.
Auto-success if the target has a visible sign of necromancy upon him (title, obvious spell, exceptionally high Divine Outrage, etc.).
Auto-success if the target is recognized as a Perverse Necromancer (justly or not).
If the target is a Necromancer, additional small possibility of success regardless of circumstance (will usually require a group of accusers to trigger).

Results of a successful accusation:
Target is unaware of who accused him.
Target gains a Forbidden Practices warrant.
Target gains a lot of Social Outrage.
Accuser gains a monetary reward, which is debted to the target.
If the target is a Necromancer, he is forced Open PvP for 2 hours (normally) or 6 hours (if seen as Perverse).

Results of an unsuccessful accusation:
Target is unaware of unsuccessful accusations against him.
If the target is a Necromancer, he gains a little Social Outrage (even if he's done nothing wrong, heat is being directed toward him).
First unsuccessful accusation results in the guard issuing a warning to the accuser.
Second unsuccessful accusation within a short amount of time results in arresting the accuser for disturbing the peace.

Further Notes:
Bards get extra money for accusing.
Clerics get devotion for accusing.
Necromancers reduce their social outrage for accusing.
Paladins get soul for accusing.
Withdrawing money from banks while socially corrupt will no longer get you arrested, joining debt payment as the only legit services to use in town, for the sole purpose of letting you get your stuff and leave town. Please note that this does not extend to all bank services.