This incarnation of the Doctor appears on the outside to be about fortyish, six feet tall, with black hair beginning to grey. If you think of Patrick Troughton, you will be doing well, though Coburn does not have Troughton's nervousness. (No "Oh dear, oh dear, oh dear" or the like.)
At first appearance, some would say he is going through a second childhood, complete with a child's attention span. Even in tight situations, he can be easily distracted by, say, a set of jacks, a yo-yo, etc. Like any child given his own, his diet is atrocious, craving sweets above all else. He loves his jellybabies! Wearing a magician's outfit complete with hat and cloak, he has absolutely no command of the skill.
This Doctor lets his impulses get the better of him at times, and doesn't always think before doing. He constantly lets his curiosity get the better of him and almost enjoys getting into trouble.
This Doctor can appear to be vulnerable, and readily admits that he does not always have the answers to everything, but is willing (and eager) to seek them out. In keeping with a somewhat mysterious aura, he never introduces himself as "the Doctor". (i.e. "I'm the Doctor".) Rather, in Colin Baker style, he always says "I am called the Doctor", or "I am known as the Doctor" or anything along those lines. He also refers to his TARDIS in more personal terms. ("She" or "her" rather than "it".) Although this Doctor is generally known for his positive attitude, there is a hint of loneliness and regret which comes out from time to time. Loneliness due to the fact that, although he constantly surrounds himself with friends and companions, he is still an exile and on the run from his own people. Regret for what is unknown. Our only hint is that that Doctor has mentioned some great sin or sins he has committed in the past. What they might have been or whether he might be exaggerating, hiding something, or whatever is left for speculation. He did, however, travel without a companion for two hundred years after Dara left because he did not feel he had the right to expose his friends to the dangers his life would bring upon them.