Working through the channel, measure the distance between the joists and cut a 2x4 to this length. Attach a fan-rated outlet box to the midpoint of the 2x4 where you want the fixture to be. Attach a joist hanger to each end of the 2x4, keeping them flush, not protruding past the end of the wood. Butting the 2x4 against a flat surface while assembling can help to keep the bracket set properly. Insert the support assembly between the joists and set it so the outlet box is flush with the ceiling surface.
Often a wall receptacle from an upper floor can be used as a source for a new ceiling fixture below, but a switch loop must be run to a wall switch in addition to fishing the cable from the source.
Thread the connector clockwise onto the twisted wires, being sure no bare copper is exposed at the bottom. Pull gently on the connector to be sure it’s secure. You can wrap electrical tape around the wires and cap for extra security or just push the splices into the back of the box and attach the cover plate.
Hold the fixture up to splice the wires. Usually the first wire splice will aid in supporting a small light, but have a helper assist with supporting a large, heavy fixture while making the connections. While still supporting the weight, attach the base to the mounting strap with the screws and tighten the base to the ceiling.