In order to breed a mule, you must have a donkey and a horse of any kind. To breed them, feed each a golden carrot or golden apple, and activate love mode. They will then run to each other and a baby mule will be born between them.
Mules are slightly smaller than their horse parent, and when they grow they share traits of both a donkey (the long ears), and the horse (color, tail, etc.).
To ride a mule, first the player must domesticate or "tame" it. Once tamed, riding is as simple as right clicking the mule, no longer requiring an empty hand. At first the mule will allow the user to ride it, and wander aimlessly. To control the movement, a saddle must be equipped. To do so the player can open their inventory while riding the mule and placing a saddle in the appropriate saddle slot on the mule's inventory.
Mules have the same usage as donkeys do. They do not allow the use of horse armor. They can carry items for the player. A mule can only hold one chest, even though it appears to have two (one on each side). A chest is simply equipped by placing a chest on the mule by right clicking.
Like horses, some mules are faster, others have the ability to jump higher, and some have more health. The fastest mule is slower than the fastest possible horse. A mule can be bred by breeding a horse with a donkey. The mule is a combination of the horse and donkey, appearing as a horse with long ears.
Advantage Over Donkey
One may ask what the advantage of a mule is when they have the same ability to carry chests as donkeys. There are a few reasons. First, the mule is colored to look like it's horse parent, which is nice for those who desire a specific color animal. The second feature is that they inherit traits from the horse parent as well. Since horses are potentially faster than donkeys, a mule can be bred with a fast horse and fast donkey to make a mule that is faster than the fastest donkey, yet slower than the fastest horse (in the middle). This is nice for those how desire speed above all else, but still want to have the option to carry more items.