Turn the power to the light circuit off and then remove the old light fixture.
Cut a hole in the ceiling with the keyhole saw at the light's new location. Use the remodeling box as a template for the size of the hole.
Run electrical wire from the old location to the new one. Connect the wires from the existing wire and the new wire together in the old box with wire caps. The old box will function as a junction box.
Screw the cover onto the junction box.
Install the new box. Run the wires through the gap in the back of the box and then push the box into the ceiling. Screw the flaps at the edges of the box to secure the box to the ceiling.
Install the ceiling fixture.