Try to unscrew PVC pipes by hand. If you can’t unscrew the pipes by hand, then use a pipe wrench or channel locks to loosen the connections.
If you find the clog in the trap, reattach the trap. Turn on the hot water and see if the sink drains. If the sink is still clogged, then follow the next steps to use the cable auger.
If the cable catches on something, then turn the handle counterclockwise and pull the auger back. If the auger meets resistance again, continue pulling the cable out and cranking the handle clockwise until the cable catches on the clog.