Download the screenpack you want to your desktop.
Unzip it, and open the folder.
Now open your mugen folder and resize both windows , so you have them both up on screen.
Simply drag and drop all the folders from the screenpack into your mugen folder.
When it asks you if you want to replace, just click yes.
This simpler method will replace the system, sound, and other files necessary to run the screen pack.
Now try it out.
Not all screenpacks work this way.
Some require more complex ways of doing it, such as adding extra lines in the system.def.
But I prefer simpler ways of doing things, so don't ask me as I don't know how... I don't have the patience to go that much in dept into mugen.
If that's the case, just download a different screenpack.