Be the Average Joe. Look the part by dressing in khaki's, a button up shirt, vest, tie, and wool jacket. Stewart is known for portraying family men, who represented the little people.
Get quaky. Stewarts voice is very distinctive. Originally from Pennsylvania, his voice was an exaggerated mid-western accent. His voice shook a little when he spoke. There was always a little quiver in every word he said. The key is to add this element, without cloaking your words.
Stewarts wide eyes were what gave him the innocent look that we all melted into. They are similar to "puppy dog" eyes. Widening your eyes while raising your eyebrows will give this effect. The point is to look innocent, not surprised.
The half smile. Give off a smile that is similar to the Mona Lisa smile. Smile from one side of your mouth as opposed to both. This gives off the "aww shucks" vibe Stewart was known for.