How do I wire a new light from an outlet, with power to the light box?
Many drawings are obsolete.  The cable from the lamp to the switch must be 14/3 cable.  This is mandatory. 

Fortunately, this also makes the colors less confusing.   


Black = always hot
Red = hot when light switch is on 
White = neutral (current return) 
Green/bare/anything metal = equipment safety grounding,  hook everything to everything else, and I won't mention grounding again.  




The switch has 2 (non-ground) screws. You attach a black wire and a red wire. This is logical since the switch decides whether hot (black) is fed to switched-hot (red).  

If the switch is a "smart switch" or modern dimmer, it may also need white - if so, the instructions will say.  If white is not used today, put a wire-nut cap on it and tape that on (they tend to fall off a single wire). 

Now look at the lamp itself.  You see it has a black and white wire.  That's a little "off color scheme", isn't it? Black means always-hot and that means the light would be on 24x7. That's just how they're made.  A red wire (switched-hot) makes more sense, don'tcha think?  That way the light would be controlled by the switch.  Just remember that weirdness...  or spend $4 on a 5-pack of colored electrical tape and mark the wire red.  

With that behind us, up in the lamp box, and in the receptacle box, just match similar colors.   Black to black etc. 

That was easy.  Power of color coding and using the right /3 cable.