Turn off the power to the circuit powering the light fixture, at the home's circuit breaker panel.
Remove the thumbscrews holding the light fixture in place. Lower the light fixture down from the ceiling.
Loosen the wire nuts connecting the home wiring to the light fixture wiring. If there are no wire nuts, you may need to cut the wires, or loosen screws on the light fixture connecting the wires.
Loosen the screws holding the light fixture box against the ceiling joist. Lower the box from the ceiling.
Cut an opening in the ceiling for the recessed light, using a keyhole saw.
Attach the home wiring to the recessed light wiring, using wire nuts.
Position the recessed light fixture in the ceiling and attach it to the joist with screws through the fixture's mounting bracket. Snap on the trim ring to the bottom of the recessed light.