Shut off the electricity to the existing fixture at your home's fuse box.
Take out the screws around the existing fixture, so you pull it part way down and get at the wires behind it. Remove the wire nuts that connect the wires between the fixture and the box. You will be left with an exposed box and a wire, a black and a bare grounding wire from the box.
Hold the mounting bracket (that came with the new fixture) up against the electrical box. Secure it with the screws it came with.
Connect the copper ground wire from the box to the green grounding screw on the mounting bracket, and tighten.
Link the wires from the fixture to the wires from the electrical box, using the wire nuts and connecting white to white and black to black. Make sure the nuts completely cover the bare wire ends, so only the insulated portions of the wires show.
Hold the new light fixture up to the electrical box, tucking the wires into the box as you do. Secure the fixture to the box with the provided screws, threading them through the screw holes in the fixture and the bracket.
Turn on the power.