Electrical – extend a cable to add another outlet

Two options:

1) Replace the ceiling fixture with a pull chain model, plus an outlet. Bypass the present switch.

2) Run a new cable from the outlet to the switch box. Your picture shows white color NM cable, so presumably it is 14/2 (black, white, ground, 15 amp maximum). Obtain more wire, and hook three wires (black, white and ground) into the respective positions in the couplers.

Read up on basic electrical safety before attempting any of this. The bottom bundle, as you wrote, is the incoming hot.

That description is OK, but you really only need to run 2-wire with ground romex up to the switch, not 3-wire. Split the hot side of the outlet as described. Use a wire nut to pigtail a short piece of wire from your source hot to the terminal of the receptacle that you want "always on" and also connect to the new black wire from the romex running to your switch. Connect the other end of your new black wire to one terminal of your new switch.

Remember, the switch just "makes" or "breaks" the hot.

Connect the new white wire from the romex to the other side of the switch. Permanently mark the white wire at the switch box with red or black permanent marker to identify it as a "switched hot". Connect the other end of the white wire from the romex to the hot terminal of the receptacle that you want switched (for the disposer). Permanently mark the white wire at the receptacle with red or black permanent marker to identify it as a "switched hot". Connect the source neutral to the receptacle and ground everything.