Makai Senki Disgaea 2/Felony System

The Sin system is opened after stage 3 or 4 (I can't remember) during the main story. At this point you can talk to the guy next to the Dark assembly person to get a paper convicting your character of a crime. Check the paper to see what level the innocent is, and that is the level the portal will be on to the trial. Such as, if the paper has a level 8 innocent on it, then go into that paper and go down to level 8 where you will see a blue gate and go through it. You can also move the level 8 (or whatever) innocent to a different item and travel down to level 8 of that item to find the gate.

You can throw in a stack of characters into the blue gate and have them all tried at once. You still only get 1 item or 1 ammount of HL though. But all of the characters will get conviction points.

I don't know the specific ammounts each conviction gives you, but I do know it helps that character gain more experience in battles and will make passing bills in the dark assembly faster overall.