I can only think of two real don't off the top of my head. Don't make it a joke. A lot of times a stuttering character is just there for comic relief, because stutters are stupid and it's hilarious (not). And don't make it a symbol of low confidence or whatever. A lot of times the character really struggles, then they get a great pep talk or complete their character arch or whatever and as a symbol of that they're now totally fluent. I wish it was that easy.