To progress the story you need to complete these 4 steps:

Visit Erzulie
Talk to the Condemned Man
Escape from Jail
Fight your way out of Port Royal

When you first arrive in Port Royal you and the crew will all be standing around. Feel free to talk to everyone. The Captain will tell everyone to meet back at the ship tomorrow at 10am sharp and will even give you his Watch so you won't be late. When everyone goes their separate ways you can head off down the street towards the Fortune Teller's shop.

Erzulie is one scarey lady, but she is loaded with info which is very valuable to your quest. Ask about everyone and everything and watch the disturbing vision in the crystal ball. Before you leave, she will give you 2 Potions, one to restore your health and another to restore your energy during combat. These are both limited so use them wisely.

As you leave Erzulie's shop you will bump into Captain Justice. After a few seconds of conversation he will be attacked and killed by a pair of those robed assassins. You will have to fight them both, but they only take a few hits each before they drop a flash-bomb and disappear. Not too long after that the Constable and some guards will arrive.

After talking with Wormius things start pointing to YOU as the main murder suspect. Then Bone shows up and says he witnessed you kill the captain. That's all it takes and you are immediately thrown in jail. Of course, this all works out for the best because now you can talk to the "Condemned Man" in the next cell. You learn that he was part of the fleet that was sent to Lizard Point to do all those horrible things you saw in Erzulie's crystal ball.

After agreeing to take him with you when you escape you now need to plan your escape. Wormius is pacing back and forth guarding the door. Open the wood table and take any of the items and clank it against the bars on the window. Anne will show up with a Bottle of Rum. When she leaves, turn around and Wormius will confiscate the bottle.

Talk to Wormius and tell him you are THIRSTY. This will provoke him into drinking the entire bottle of rum right in front of you. Naturally he passes out leaving you to work on your escape. Take the spoon from the table and use it to loosen the rocks under the window. Take the Rock and turn to face the room. Throw the rock at the rack of guns along the right wall. This will trigger a small animation which will send the keys flying over to your cell.

Unlock the door and reclaim your Inventory Chest from the corner of the room. DO NOT try to take the gun from the table or Wormius will wake up and kill you. Free the Spaniard and head for the door. SAVE YOUR GAME before going through the door.

Once outside, a guard immediately spots you. He will kill the Spaniard giving you just enough time to draw your sword and gun. During the next action segment you will need to kill many guards very quickly. You have unlimited ammo so keep firing and always keep spinning to catch the guards who sneak up behind you. Watch for the guards on the rooftops, and if somebody gets in too close just use your sword to slice them up. There are three combat areas all separated by a small animation. The final combat ends with you backing into Bone and him punching your lights out.

You wake up back on the ship and are immediately put on trial for the murder of the captain. It is also brought out into the open that Sullivan is actually a girl (much to Lyle's relief). Since nobody really likes Bone, they manage to get you a lighter sentence. Instead of being hanged, they dump you and Anne into the ocean and sail away. Just your luck, you wash ashore onto RedJack Island.