Go into your ICBC agent. They will need to visually confirm the original vin on your frame or your body - which ever one wasn't swapped out. If you got no original VIN on the frame or the body after the swap you could be in a bit of a pickle with ICBC. Say the VIN stamps are no longer legible on the frame and you are going to do a body swap, then you might want to speak to ICBC before doing it. The ICBC agent need to visually confirm one of the VINs or you are SOL.
You will do the paper work at the ICBC agent office. If they are nice. They will call ICBC and fax it through. The paper work also has to be mailed with a cheque from you - so bring your cheque book. You will have to name and give the address for a licensed inspection facility which will receive the BC VIN plate. When the inspection facility gets the plate, they will call you and you bring in the vehicle to have them put the VIN plate on the door pillar. This cost me $40. Some charge a lot more. You can also have them stamp the VIN on the frame as well. That would add to the cost.
Of course, if you didn't want to follow the letter of the law and you were just swapping a clean body over to a good frame and running gear, you could carefully drill out the VIN plates and re-rivet them yourself. However, if you are pulled over, and the peace officer suspects the VINs have been tampered with, you would be in a bit of trouble.