The gooseneck (shower arm) is the bent part coming out of the wall. On some older versions, it has a ball integrated into the pipe, so you won't be able to remove the head!
If you pull the round plate (escutcheon) away from the wall, you can use a pair of channel locks to remove the entire assembly (arm and head). Examine the head. If it is threaded onto the arm, use the channel locks to unscrew it while holding the arm. Be careful not to slip because you can damage the finish on the metal. (You know turning leftward loosens the head)
If you want to clean the head, soak it in CLR for 15 minutes, allowing the chemical to dissolve the mineral deposits. If you want to replace the head, use teflon tape on the shower arm (3-4 turns) and screw the new head on.
Apply teflon tape to the back end of the arm (3-4 turns) and screw it in place. (Remember to put the escutcheon plate on BEFORE screwing the arm into the wall).
Drop your clothes and take a leak-free shower! Woo HOO!