That's all there is to it!
The longdesc attribute of the img tag allows you to associate a longer description with an image in HTML.
If your description is located at my_description.txt then your full img tag would be as follows:
<img src="my_image.jpg" alt="descriptive phrase" longdesc="my_description.txt">
The following image has both an alt attribute that reads "puppy" and a more descriptive longdesc attribute that describes important features about the photo including that the puppy is very young and small enough to be held in someone's hand.
That's all there is to it!