Talk to the Sea Hunter for the first time to start this quest, and choose Captain's Charm. He will say the following:
You there! Are you here to join the Sea Hunter's Guild? You look like you've never heard of it... Well, I can't say I'm surprised.
We used to be well known in these parts but I'm afraid over time our numbers have dwindled. Although it's been disheartening, it is my full intention to restore the guild to it's original state.
If you're looking to help, I could use someone like you. Though you're going to have to prove yourself first. I can't just let anybody join. I want you to prove your might by taking down a Pirate Captain. He will likely be carrying a charm on him. Bring that charm to me and we'll talk guild membership.
Upon starting the quest, the Pirate Captain's Charm will have a chance to drop from any Pirate Captains encountered on Pirate Islands. It has a high drop rate so kill a few of them until it drops, then return to any Sea Hunter to finish the quest, by choosing the same dialogue option. He will say the following once you finish the quest:
Ah, so you've done what I've asked. Good on you, and welcome to the guild!
I think it's safe now to let you access some of our wares.
We've been stocking up all kinds of items for years now. Since you are merely an initiate I can't trust you with our best gear, but continue to prove yourself and I'll consider it. As you rank up with the guild I'll give you access to new and better weapons, armor, and other items.
In order to rank up, complete the tasks I ask of you, without question. Your loyalty will be rewarded.