Open up Radiant, open your map, and let's get started!

The Surroundings

 1. Select the map background you want from the list of materials. It can be anything you want, it doesn't matter.

 2. Draw however many squares it takes to surround your map with the background image.

NOTE: Make sure it's touching the ground. It shouldn't be lower.

3. Fix the height. Make sure it stays on the ground while you raise it to about 1024. If you have any buildings or prefabs or whatever already at that height, it should be higher. You should now be surrounded by the sky you added when your in your map.

The Skybox

4. Now we need to add a skybox. Draw a box over the playable area and the playable area ONLY! It should be touching the surrounding boxes, but they shouldn't overlap. Raise the box to 1024 (or however high you set the surrounding boxes)and DO NOT let it stay on the ground. It should be a thin box, not like the surrounding ones, and should only take up the space at 1024, nothing lower, and higher being acceptable if it meets the surrounding boxes.

Save, compile your map, etc. and then run it.

The Groundbox

5. A groundbox is optional. If you want people to fall forever under the playable area, then you might want this so they can be entertained until they pass it. :P

6. Anyways, this is very simple. Draw a box just like you did with the skybox, but MOVE IT RIGHT UNDERNEATH THE PLAYABLE AREA! Again, this should meet the surrounding sky background. If it touches or is above playable area of the map, that's bad. It shouldn't touch anything, only meet the surrounding boxes. Of course this would be in the negatives.

There you go! You now have a box surrounding your map! No more black nothingness.