This page contains several diagrams for wiring a switch to control one or more receptacle outlets including a split receptacle and multiple outlets wired together.
This diagram is similar to the one above, but the switch comes before the new light in the circuit. New cable is run from the receptacle to the new switch location and from there to the light location. The switch may also be added in the the same box with the receptacle as in the diagrams at this link, where the two are installed in a double-gang electrical box.
Lamp cords are usually one color, making the standard black-hot, white-neutral guidelines useless for determining polarity. Other methods are therefore used to determine the polarity on a lamp cord. Check the insulation on the cord wires closely and you will find either a textured bead or a thin colored line running along one wire, this is the neutral.
The white wire on the switch loop is used to carry current from the source to the switch and it is marked with black tape or paint to label it as hot. The black on the switch loop runs from the top switch terminal to the top half of the receptacle. With this arrangement the top half of the duplex is controlled with the switch and the bottom half is always hot.