Cut electricity to the existing fixture at the house circuit box.
Lower the old fixture by removing the screws holding it to the ceiling electrical box. Disconnect the wires that are above the fixture so you can pull it away completely. You should be left with an exposed electrical box and a black wire, a white wire and a bare grounding wire coming out of it.
Hold the mounting plate from the new fixture to the electrical box. Secure it there with the provided screws. Pull the wire ends down through the holes. (Note: Touch the plaster around the box as little as possible, as it's likely brittle.)
Twist the bare grounding wire around the green grounding screw on the mounting plate and tighten it.
Hold the light fixture up to the electrical box. Hold the white wire from the fixture next to the white wire from the box and twist them together with a wire nut. Wrap the connection in electrician's tape. Connect the black wires in the same manner.
Set the fixture up against electrical box. Line up the screw holes. Secure it to the bracket with the screws that came with it. The fixture should cover the whole area around the box where the old light was, including any discolored plaster there.
Turn on the power.