People often use the word bemuse when they mean amuse, but to amuse is to entertain, and to bemuse is to confuse. In Alice in Wonderland, the White Rabbit amuses Alice as he frolics, but then the Cheshire Cat bemuses her when he tells her to go two directions at once.

To amuse someone is to make them laugh or otherwise keep their attention. It's often used in the negative — if someone says that a joke does not amuse her, duck before you get slapped. In the movie Goodfellas, a tough guy says darkly, "...I'm a clown? Do I amuse you?" Here are friendlier examples:

There's nothing spellbinding left to amuse our children. (Forbes)

This was fashion as theater and an often amusing way to end Paris Fashion Week. (New York Times)

To bemuse is to confuse or muddle, and it's almost always in the form bemused. It sounds like that other word, but it's not as fun to be bemused. These examples get it right:

Another father seemed bemused that his son had been taken in by the police after he went for a walk on Saturday.  (BBC)

In the past, reviews of Bosco's dazzlingly vivid apparel and sneakers have ranged from admiring to bemused to scathing. (New York Times)

The passengers, bemused at first, were quickly won over once they realized who was performing. (Time)

It's no wonder people get them mixed up — both words are derived from the French word muse. It's just like a French muse to entertain and confuse us all in the same root word.