Turn off the electricity to the kitchen by flipping the circuit breaker to the "off" position.
Remove the old dome by removing the screws from the base, if there are any, or turning the dome counterclockwise to remove it from the ceiling. Let the dome hang.
Touch a non-contact voltmeter, available from all hardware stores, to the covered plastic portion of the wires hanging from the ceiling. It should read there is no voltage. Check the circuit breaker if there is voltage present. Call an electrician if the breaker is in the off position and there is current in the wire.
Unscrew the wire nuts to remove the dome light from the wires hanging from the ceiling.
Take out the screws holding the mounting bracket in place and pull the mounting bracket from the ceiling.
Remove the screw from the center of the electrical box. Cut a length of bare copper wire, about six inches long and wrap the end of it around the screw. Tighten the screw down into the electrical box with the copper wire attached.
Mount the new bracket on the ceiling by inserting the screws included in the kit. Assemble the dome light according to the instructions.
Connect the wires from the dome light to the wires hanging from the ceiling. Connect the neutral wire from the dome light, indicated in the instructions, to the white neutral wire coming from the ceiling. Connect the unmarked wire to the red or black hot wire coming from the ceiling and attach the ground wire from the light to the bare copper wire in the box. Make all connections by turning a wire nut over the exposed ends of the two wires.
Feed the wires up into the ceiling. Screw the dome light casing onto the long bolt hanging down from the mounting bracket. Turn on the circuit breaker and test.