The switch in this room controls the ceiling fan and a half-hot outlet. I would like to convert the half-hot outlet into a full-hot outlet and continue using the switch for the ceiling fan. I've included pictures the switch and the receptacle. I'm not familiar with how this is wired (white being used for power?) and could use some pointers.
Update: I followed the instructions @RMDMan gave in his answer and the result was that the outlet was always hot, the fan didn't work, and the light switch didn't work. I'm wondering if I did something wrong. The wiring after I followed the instructions is as follows:
I tried a few other configurations which led to different scenarios, none of which were the desired outcome. For example, one configuration led to the fan working, no power going to the outlet, and the switch not working. Some configurations also led to no power going to the bathroom next door.
This led me to believe, and I'm probably wrong, that the black wires work as follows: one black wire is hot (the one with the white dot in the picture below), one black wire carries power downstream to the bathroom, and one black wire along with its corresponding white wire come from the light switch as part of a switch loop.
The current state is in the picture below. This gives me an always-hot outlet, a working fan, but a light switch that doesn't work.
What could I be missing here?