It's probably the most asked question on the forum.
If you take a look at a model like
this one, you'll notice it reads "skins" somewhere. In this example you can see that there's a red sentence that reads "Textures\BGIIPiano.blp" or something like that. It means that included in the model there are 1 or more .blp files. Those files are SKINS. When importing the model, you must also import those .blp files, and more important: in the IMPORT MANAGER, you must change the PATH of this texture to the red sentence.
To follow the piano example: you must import "BGIIPiano.blp" into your map, and then double-click this file in the import manager. Next you change the path of this file into "Textures\BGIIPiano.blp".
Whenever a model shows up as a green/black checkerbox, you probably didn't change the path of those textures.
Note that, after importing a model, you need to refresh the textures. To do so, save your map and either restart World Edit, or alternatively, save your map and go to "File, preferences, video" and then change your texture preferences to medium, high or low. The textures will be refreshed then.
