Senior mod makers will be using the Jass NewGen Pack (
http://www.wc3c.net/showthread.php?t=90999) which allows for the modder to do a lot more editing, but the World Editor has a built in way of changing around tilesets, though it is very limited.
In your toolbar, go to "Advanced -> Modify Tileset."
You are allowed 12 maximum texture space, with each tile occupying either one or two texture space(s). Check the "Use custom tileset" box and you can begin adding tiles from other sets, assuming you have the space. If you don't have the space, you must remove one of the tiles you already have. Cliff tiles (with the red squares in the corner) cannot be added or removed.