Hi, M.,
My son also started stuttering when he was about 3 years old. It started suddenly and was quite pronounced, involving tics of him moving his hand next to his mouth and then moving it downward from his mouth as if he were physically trying to push the words out of his mouth. I took him to a speech language therapist and was given similar advice as Gretchen in a previous post did and that proved to be quite helpful.
Being a Marriage & Family Therapist, I also know that sometimes stuttering can be triggered by a stressful event for the child. After thinking through what could have happened to my son just prior to the onset of his stuttering, it finally dawned on me that when my Mom came to visit us the week it started, she had said something to the effect that she just loves him so much, she's going to pack him in a suitcase and take him home (to FL) with her.
Realizing that kids this age are extremely concrete thinkers, I suddenly realized he may have taken her quite literally. I sat him down and asked him if he remembered her saying this to him (this was after she had gone home from her vacation already). His response was to get teary-eyed and he said he wanted to stay and live with me and Dad! Poor little guy! After I reassured him he would always stay living with us and that Ma (what he calls my Mom) just meant that she loves him so much and misses him so much that she wishes he were with her more often, he suddenly stopped stuttering so profoundly!
Stuttering is also genetic, and my son still, at 5 1/2 still has difficulties with pronouncing words and strangers still have some difficulty in understanding him (he was diagnosed with Phonological Disorder). He was assesed in Kindergarten last year and started Speech Therapy through the school district. By the end of the school year last spring, he was pronouncing his words much more succinctly and was more understandable. He started stuttering a slight bit more over the summer without the continuation of speech therapy, but now that the school year has started again, I know this will improve again once he starts the sessions again. He is now in 1st grade and this has not affected his learning abilities one iota. He even was voted the Most Improved Reader of his Kindergarten class at the end of the year!
Hope that helps and is of some reassurance for you!
Take Care,
S. Wolf