This tut will assume that you know "The Basics"

1. Open Hammer Editor
2. Open your map you want to add a skybox to, or make a new one and do the skybox after you've made it. Pic
3. "Browse" the textures and find "skybox" (Type it into the filter) You'll find it at the very bottom. Pic
4. Make a box around your map. Make sure you encompass the whole map. Pic... and hit "Enter." Pic
5. In the top left box (Camera box) click on the skybox and on another window, right click it and select "Make Hollow." (Select OK)
6. Pic Now you're able to fly inside your skybox. Good for you. Now, when you go in to CSS and run your map, you will see a sky.
7. Don't know what sky you want? Don't know how to change the sky? Keep going, you twit.
8. Go up to "Map" on the toolbar, and select "Map Properties..." Pic
9. This will appear: Pic... Where it says "sky_day01_01", is the kind of sky you have on your map currently. To change it, here is a site with all the names you can use listed: Wiki - Sky List
Note: Just ignore all the numbers below the picture of the skys, that's for more advanced stuff, that I've only figured out recently.