Turn off the light switch that controls the recessed lighting or turn off the power to that room if you can't access the switch.
Unscrew or snap out the outer ring around the lighting fixture that protects the bulb.
Unscrew the bulb from its socket if you can get a firm grip on the bulb, which may be difficult if the bulb and the socket opening are close in size. Press the middle of a piece of duct tape to the bulb if you can’t grip the bulb with your fingers alone. Press the two ends together to form a handle and twist it counterclockwise to dislodge the bulb.
Screw in a new bulb of the same wattage as the old bulb by inserting the end into the socket and twisting clockwise. Replace the outer ring. Restore power to the socket or flip the switch to ensure the light is working.