I am currently in Shenzhen. How do I go to Shantou island resort from here?

You can take a direct bus to reach ST city at Shenzhen Luohu Bus Station, Qiaoshe Bus Station or Futian Bus Station. It will take you to the local General Coach Station.
Well, do you refer to Nanao Island Resort of this city? If so, three buses are scheduled at the General Coach Station to the island at 8:20, 12:00 and 14:00.