This page explains how you obtain the DIY recipe for the Golden Shovel.
Once or twice a week, Gulliver/Gullivarrr will wash up on your shores and require assistance. If you help him fix his communicator 30 times, he will send you the DIY recipe for a Golden Shovel in the post! For more information on how to help Gulliver/Gullivarr, head over to the Gulliver/Gullivarrr page.
The Golden Shovel requires 1 shovel and 1 golden nugget to craft it. The shovel required is made from a flimsy shovel and an iron nugget, and the flimsy shovel is made from 5 hard wood. Gold Nuggets are obtained from boulders but they are rare and will not spawn that frequently.
The Golden Shovel is far more durable than the other shovels in the game, however, it is not indestructable. Other than its increased durability, it does not have any special powers.