I'd like to know the best  way to make a skybox, because obviously, whenever I put a skybox in my map it looks like there's an apocalypse going on in the sky.  Like really, someone please tell me wtf is this. 

It'll look fine in game if that's what you're wondering.

Alright thanks. Once again, Radiant has failed at visuals.

You'll get used to it on radiant:D
As long as you have your hollowed brush with the sky-texture applied you shouldn't have any problems ingame.

I had exactly the same problem and as Alerion said, with a brush hollowed much more big in height and width than your map you must apply first caulk texture to this brush, select all the internal faces select a sky texture and apply to this faces and with the brush deselected, press n and in skybox you must to put the same texture than in the internal faces.
Probably you cant see the skybox but after save map and you back to load map you can see the skybox correctly.