OK there are (I think) two programs used for making skymaps, 3DSmax and terragen, the former being expensive but better, and the latter being free but not quite as good. I have only used terragen so I will concentrate on that. The website is
http://www.planetside.co.uk/terragen/ and there are tutorials and example work linked from there. Basically you create a terrain by adjusting a bunch of settings, then set the sea level, sun angle/elevation, and generate the clouds. Once this is done, there are
loads of settings that adjust how the light diffuses through the atmosphere, the cloud colour, sunlight colour, shadow colour, everything. There is a preview window which helps you get the look you want.
When you have got what you want, you move the camera to a point of your choosing, setting the field of view to 90 degrees, the camera angle and elevation to 0, and do a full quality 256*256 render of that. Then to get the other 3 sides, change the camera angle to 90, 180, and 270, then back to 0 again but with elevations 90 and -90, to produce the top and bottom of the skymap. After all 6 images have been produced and saved, you have to name them skynameup, skynamedn, skynamelf, skynamert, skynameft, and skynamebk.
I can't remember exactly how half-life orientates the top and bottom images, so these may need to be rotated. Not that it matters now because my plan of getting some snarkmarks by writing a half decent mini guide on skymap creation in teragen that might have been marked as a 'correct/accepted answer' has been spoiled by the fact that I don't have the option to set this as an answer to the question. I probably did something wrong. Nevermind.