To receive sensations from his artifical hands, four main nerves that normally connect to the arms were re-routed to muscles in Sullivan's chest. Electrical signals are sent from the hands to a plunger on the chest. The plunger presses the skin which stimulates the nerves underneath, thus sending the signals to the brain.
Similarly, to send commands to his arm, the movements of his chest muscles are picked up and converted into arm movements. He can't yet do intricate tasks like tying his shoes, but he can shave with an electric shaver.
Interestingly enough, the final cost of the bionic arm, once perfected, is expected to be $6 million.
More information can be found at the RIC web site as well as here. There is an official news release, but it is pretty sparse with details.