Laughing can sometimes be completely involuntary and involves a complex series of muscles, which is why it’s so difficult to fake and also why an active effort is required to suppress laughter.
In the face, the zygomaticus major and minor anchor at the cheekbones and stretch down towards the jaw to pull the facial expression upward; on top of this, the zygomaticus major also pulls the upper lip upward and outward.
The sound of our laugh is produced by the same mechanisms which are used for coughing and speaking: namely, the lungs and the larynx. When we’re breathing normally, air from the lungs passes freely through the completely open vocal cords in the larynx. When they close, air cannot pass, however when they’re partially open, they generate some form of sound. Laughter is the result when we exhale while the vocal cords close, with the respiratory muscles periodically activating to produce the characteristic rhythmic sound of laughing.
The risorius muscle is used to smile, but affects a smaller portion of the face and is easier to control than the zygomatic muscles. As a result, the risorius is more often used to feign amusement, hence why fake laughter is easy to detect.