A rivet extractor or chain-tool has slots to hold the chain, a handle, and a punch driven by a screw. Most have two slots to take the chain. The further slot from the screw is to break a chain and to join a chain, the nearer is for loosening stiff chain-links after they have been joined.
Select where you want to break the chain. Unscrew the punch clear of the slots and put the link you wish to open in the further slot.
Break the chain
Screw in the punch until it touches the head of the rivet, ensure the punch rests in the centre of the rivet head and that the other end of the rivet is not trapped by the body of the tool. Screw the punch into the tool to drive the rivet out of the front plate and through the rear plate.
Don’t Go Too Far
When the rivet is almost through the rear plate, retract the punch and break the chain by flexing the link with your thumbs on the flat side. Check sooner rather than later to avoid forcing the rivet right through the back plate. The ideal is to leave the rivet slightly protruding on the inside of the rear plate to help locate the hole when you’re reconnecting the link.