how do i make a light switch turn on a lamp plugged into receptacle
The red wire may be a switched hot. The best way to find out would be to remove the black wire with the power off put some tape on the black and with the power back on see if this is now a switched hot. If it is great turn the power off break the tab and put the black back on.

If nothing happens pull the switch and see if the red is connected in the switch. I would guess the black is the always hot and someone changed the receptacle without breaking the tab so it is always hot.