First if you google this you can find some good information as Arm Wrestling is a well supported sport! You even catch it on ESPN and ESPN-II. Most of these guys do workouts that are a kind of blend between power lifting style workouts and body building style.
So you should work the big compound movements first really heavy like around 6X6 for the things like Squat,Deadlift,Standing Shoulder Press,Shrugs,Barbell Curls,Flat Bench, decline and incline bench, various rowing movements, wrist curls and reverse wrist curls,thors hammer with free weights etc..........
Then you need to pick assistance type exercise's like various isolation type movements done with dumbellsusuly in the 10-12 rep range and sets of 4-5 on each.....
Some guys like to toss in Olympic Lifts like the Snatch used to be done with barbell but more and more of these guys are useing Kettlebells in place of barbell for the Olympic movements which is the corner stone of their ballistic element.
Most of the really competitive guys look like they could almost be body builders except they are truly as strong as they look and they tend to be rock hard.