Sit on the wooden chair carefully and listen for where the creaking comes from.
Tighten the screws in that area using a screwdriver. In some cases, a creaking chair is simply due to a single loose screw.
Remove any screws that spin in their holes. This means that the screws are stripped and should be replaced. Replace them with screws that are of the same size or slightly larger if the hole has expanded.
Test the chair to see the creaking has stopped.
Puff some powdered graphite into the joints where the creaking is occurring and rub it into the joints with your fingers. This lubricates the joints and quiets any noise.