The first option that might come to mind is the use of onomatopoeia. For instance "words" like "Heh heh", "Ha ha", "Tee hee", and so on can indicate laughter. Unfortunately these word-sounds have several drawbacks: "Ha ha" is usually associated with an evil villain (With a victorious "Ha ha!" the villain finished securing the rope that bound the girl tightly across the train tracks), "Heh heh" can lead to pronunciation problems (e.g. is it "hay hay", "hee hee", or "huh huh"?), and finally, "Tee hee" is commonly associated with a giggly teenage girl.
So what options do we have now? As a writer, I prefer to use descriptive phrases that tell the reader how my character is laughing. Terms like "chuckled", "snickered", "hooted", "howled", and "roared" often do the job better than the use of onomatopoeia.
The final path to take is to stick with the plain "he laughed" "she laughed" terms and then describe to the reader what it is that makes your character laugh.
Laughter is a highly addictive, positive, contagious: if somebody starts, it’s very difficult to stop.