Flip the circuit breaker in the breaker panel that corresponds to the recessed lights to the "Off" position. This is for safety's sake.
Position a stepladder underneath the recessed light. Balance yourself on the stepladder.
Pry the recessed light fixture's ceiling trim cover off the fixture opening. Unscrew and remove the lightbulb. Fold a strip of duct tape back over itself and stick it to the bulb, if you are unable to insert your hand into the fixture to remove it. Twist the duct tape to unscrew the bulb along with it.
Use a non-contact circuit tester to confirm that the power is off. Reach up into the lightbulb's metal housing and loosen the wing nut. Slide the unit down or up, and tighten the wing nut.
Screw the lightbulb back into place, and reinstall the trim cover.
Flip the corresponding circuit breaker to the "On" position.