There are different degrees of laughing that need to be described in a different way so that the reader doesn't confuse one type of laughter with another. Some, start with a little smirk, and others start out-wide explosive and unconstrained.... And every person does it their own unique way too.
How would your describe different laughs... and do you actually write the words/vocal-sounds of laughter, let's say in a novel?
"Ha-ha-ha," he burst laughing.
He burst laughing. -- emphasizing on the burst, instead of the actual vocal sounds.
And, can someone give example of that type of little burst of laughing that many people do with their mouth closed. I don't even know how it is called; the best way I can describe it is, imagine you are in a quiet office environment and you see something funny: You burst, but just for a second, because you know you shouldn't interrupt the silence... and you never open your mouth in the laugh; it almost sounds like you are clearing your sinuses, or throat.