How do you make a sky without it checkering the texture all over the side of the box? I've read the tutorial several times, and I still can't see what I'm doing wrong.

What do you mean all over the side? Is your skybox not showing up in game or something? What's it doing?

Hi!
To make a skybox work properly in the game, you'd need to texture your skybox (in the editor) with the shader for that sky texture.

If you select the "skies" texture subset, you will notice there are loads of textures that make up a sky but you'll also notice there are quite a few shaders, as in those red and black checkered textures or they can also be displayed as a light blue texture with "SKY" written on it. Anyhow, you're supposed to texture your skybox with one of these shaders, rather than the real textures themselves...
So, suppose you want the Kejim Outpost skybox, then make a skybox around your map and texture it all with the "kejim" or "kejim_light" shader, and in-game, it appears as a sky!
The shaders with "_light" after the real name mean that they will light up your environment as if it had a real sun. Shaders with no "_light" after their real name will require you to either use ambient lighting or light entities to light up your environment, including outdoors...

Hope this helps!

Kayron James Mercieca - JK2 Mapping

I tried doing that, but when I entered my level, all I got was the off-white color you get when you go outside of the normal level on noclip.

Hmmmm...
Maybe the sky you're using is f**ked up no?
You can try another sky, I know the "artus_light", "kejim", "kejim_light", "bespin" and "yavin" skies work properly...
If you change the sky to another sky, do you get the same problem?
In that case, delete your entire skybox and re-create it...

Kayron James Mercieca - JK2 Mapping