This one is provabley the quickest to do, but since i have to fill this area with a minimum of 300 letters, you will find that I will rattle on for a bit.
Ok, moving on...
Before anything else you must obviously download a stage, and unzip it, so you have just the two files in the stages folder.
It must contain a sff and a def file.
Open the def file and make sure that the sff file path states exactly to the stages folder and the def file it self, assuring both names are the same.
Copy the stage name and do the following:
1 - Open your data folder, and open select.def.
2 - Under the [Characters] section, follow the example bellow.
So what it means is that the character name goes first, separate by a coma symbol, then stages, forward dash, stage name.def.
Character name, Stages/stage name.def
3 - Save and it's done!
NOTE that it only works when you're fighting one on one, when you go on team modes, mugen cancels it out and you'll play various characters in the same stage... Usually is the last opponent's stage for that round.
To add stages for general use, add them in the select.def under the [Stages] section.