To unlock the Wandering Trader, go into your skills menu and obtain the Trader 1 Skill.
Once done, a Wandering Trader will visit your island and offer you special deals!
The Trader will initially offer you two deals, and visit your island about every 40 minutes.
With the Trader Skill upgraded to level 2, he will visit twice more frequently.
At Skill level 3 he will offer you four deals on items, and at level 4 he will lower his prices by 20%. The prices he offers depend on your gold/sec.
The Wandering Trader will offer you one or more of the following:
The amount for each deal will vary, for example, you can get 1 level of Golem and 33 of Spider.
Premium users will have the option to refresh the listing once per visit if they want to try their luck at getting better deals.
If you buy everything from the Trader he will leave right away, otherwise, he will hang around for a few minutes before leaving.
Treasure Map:
The Wandering Trader is the only way to get Treasure Maps. https://www.youtube.com/watch?v=7VFmMgtrHQ8
Once purchased from the Trader, a Treasure Map will appear in your offhand with an X marking a spot on your current island. You will also receive a wooden shovel. When you reach the location the treasure is buried in (shown by black smoke above the block), right-click the block with the shovel to get rewards. Possible rewards include: Schmepls (~100), Exp(~30), and Powerup parts.
Example image of Trader offers: