Turn on the recessed lights so you can tell when the power shuts down then go to the household circuit panel. Switch the breaker for the lights to the "Off" position. Give the lights time to cool down before continuing.
Climb up a ladder, if necessary, to access the recessed light. Remove the bulb by turning it counterclockwise until it comes free.
Slide a flat head screwdriver under the edge of the casing and pull downward to create a gap between the casing and the ceiling. Push your fingers under the edge and pull down until the casing comes out.