ug, it took me forever to get an explanation of this that I understood, so let me try to help you out a little.
in the areas where you want the player to be able to see out into the sky, you place brushes completely covered (all sides) with the SKY texture. This is NOT a texture that looks like your actual skybox or something, it's just a small light blue texture. What this does is tell HL that that brush is special- rather than see the brush, you will be able to see through it into the sky- made of tga files in the gfx/env/ folder. so, the images you actually see far off in the distance are not textures in your wad, they are special files in gfx/env/. you choose the sky your map will have by putting its name in Map Properties. If you want the sky to give off light, add a light_environment entity to your map (it can be anywhere, so long as it's inside the map, ie not a leak). That lets you set the angle and brightness of the light from the sky.
that's quick but hopefully it will get you in the right direction. the main thing is that you understand that it is an optical illusion.