You must have at least two folders on your screen to do this.
You must do this quickly. What to do is double click the home button and tap on a folder and hold it until it goes into the screen showing you your opened apps. The folder you tapped should be gray.
Next you go back into the app screen. The folder should still be gray and everything still should be jiggling.
Tap on the folder you want to put the folder in. The gray folder should be on the side of the folder you want to put it in.
Next you drag the gray folder into the opened folder. Voila!