Turn off electricity to the old fluorescent light fixture at the house fuse box, by unscrewing the fuse for the circuit. If the circuit is on a breaker instead of a fuse, turn off the breaker.
Take the fixture off the ceiling by removing the screws that hold it to the ceiling electrical box and disconnecting the wires behind it, exposing the box completely.
Mount the installation bracket from your new light kit to the ceiling electrical box, using the provided screws, threading them through the screw holes.
Affix the bare copper ground wire from the electrical box onto the green grounding screw on the mounting bracket and tighten the screw.
Hook up the other two wires from the electrical box to the two wires from the new fixtures. Hook up the wires black to black and white to white, making each connection by twisting a wire cap over the two wire ends together.
Raise the new light fixture to the ceiling box, tucking the wires into the box as you do. Affix the fixture to the box with the provided screws. Turn on the electricity.