This type of switch will be referred to as a 2 circuit lamp switch when shopping at home stores. Don’t mistake this for a three way switch (pictured below), the two do not function in the same way.
This page contains wiring diagrams for adding a new light fixture using an existing receptacle as the source. Diagrams include adding a light from a switched receptacle and tapping an always-hot outlet. Different wiring arrangements are included to allow for either the light or the switch to come first in the circuit.
This is a wiring diagram for an antique floor lamp with 4 bulbs, one main bulb and 3 peripheral, and usually smaller bulbs. The main bulb threads into a standard socket with an integrated switch and the three peripheral bulbs are wired to a single switch. The secondary switch may have wires colored black, blue and red or, if it’s an old switch, other colors or texturing may be used to distinguish them.
Here a receptacle is added to a 3 way light circuit before the first switch. It is not controlled with the switches but is instead always hot. The source hot, neutral and ground are spliced to a 2-wire cable that runs to the new outlet. The 3 way switches and light are then wired in the usual way with the common on SW2 spliced to the source hot and the light hot wired to the common on SW1.