2D skyboxes are very easy to make and are essentially walls with the skybox texture applied to them, in game it is rendered as a sky.
The brush must have the tools/toolsskybox texture applied to all sides in order to work correctly and the sky type can be applied using the correct skyname (see HL2 skies list) in the Map Properties->Skybox Texture Name.
Many people just drag a ceiling brush over the map and apply the sky texture to it, this would work but doesn’t give you room to expand upwards so it’s a better idea to leave some room, it won’t cost you anymore resources to do so as the skybox texture hardly makes any difference to the level resources.
As you can see it’s very simple to do and if you add a light_environment somewhere in the level it will light the areas of sky for you.
Another useful part of this method is when buildings are created at varying heights you can make them all fit neatly in with the skybox, have a look at my (very crude) street example.
That’s basically it, don’t ever drag a box around the whole map and hollow it as it will cause VIS to render the outside of your level as well and waste level resources. Think of them as normal walls and seal the level as usual.