Turn off power to the old fluorescent light fixture at the fuse box of the house.
Unscrew the mounting screws that hold up the fixture. Lower it and disconnect the wires from above it. Discard the light, leaving three hanging wire ends from an exposed standard electrical box. The wires should be black, white and bare copper, which is the grounding wire.
Hold the mounting bracket that came with your new fixture up to the electrical box. Attach it there with the provided screws.
Twist the bare ground wire around the green ground screw on the mounting bracket. Turn the screw clockwise to tighten it.
Connect the black and white wires from the new fixture to the black and white wires from the electrical box, twisting a wire cap over each connection and turning it clockwise.
Lift the fixture to the ceiling, pushing the wire connections into the electrical box as you do. Align the screw holes between the light and the bracket. Screw in the screws to set the light.
Put one or more CFL bulbs in the sockets (depending on the design of the fixture), turning them clockwise to get them in. Don't over-tighten, as it could break the bulbs. Turn on the electricity.