To progress the story you need to accomplish 3 main goals in Lizard Point:

Find a Sword
Learn to Fight
Prove yourself by defeating the shark

You should also talk to everyone until all conversation possibilites are exhausted. It also helps to return and talk to these people after certain events as new topics will be added to the conversation topics list.

Your adventure begins at Lizard Point. As you head toward town you will notice hooded figures lurking in the bushes. Do NOT investigate or return to the woods at this time or you will be killed by the deadly assassins.

About halfway down the path you will find a house (your house) to the right. Inside the house is your brother Jake, who will give you a hard time about not having a job. You can talk before heading into town if you wish.

To the left, directly across from the house is a path leading to the beach where you can find Lyle camping behind a rock. You should probably save this encounter until after you have visited the town.

The first person you meet in town is Anvil, the Blacksmith. You can talk to him until there is nothing left to say then go talk to Elizabeth. Listen to her problems and her possible solutions. When you are done talking with her you can head for the tavern located to the left of her and across the bridge.

Inside the tavern you can talk to the bartender and eventually you will be directed to talk to Captain Justice. He is looking for help and offers you a job if you can prove yourself worthy.

When you leave the bar, head around to the right of the building and go through the side door into the cellar. Grab the bottle of Rat Poison from the shelf then return to the town circle.

Off to the right is the fish monger, Shaggy. He will talk to you and eventually give you a pail of chum to help you attract the shark. Now head out to the pier and talk to the the two pirates, Bone and Cross. Bone is a jerk and will try to pick a fight, but Cross will step in a offer some friendly advice.

As you leave the pier you can turn to your right and go up the hill to the lighthouse. Inside is a broken down staircase and a trap door that leads down to a cave with a chest. The chest contains a pistol, sword and a letter from Jack Redding. Take the weapons and read the letter. As you close the chest a ghost of Jack will appear to give you lots of valuable background information. He will vanish when he is done talking.

Now its time to go find Lyle who is camped out on the beach. Be careful when going through the wood. If you go past the path to the beach the assassins will kill you. A series of planks extend out over the water to a large rock. You can go out here for a closer view of the shark, but you are going to need a boat to actually kill it.

Lyle will try to scare you when you pass by the campfire. Talk to him until he doesn't want to talk anymore. He has lots of good advice and will be one of your best friends. When he is done talking to you, "borrow" his rowboat and head out towards the shark.

When you are a short ways from the beach you will see a small movie of the shark circling. Open your inventory chest and combine the Rat Poison and the Chum then toss the pail into the water. If all goes well you will have one dead shark which will float onto the beach and be waiting for you when you get back. If you haven't already been to the cave under the lighthouse, you can row the boat forward a few times and float into the cave to get the items from Jack Redding's chest.

Back on the beach examine the shark and get the Shiny Tooth as proof of your conquest. You can talk to Lyle again or just head back into the woods. You will get jumped by the assassins but Lyle will step in to save the day. He will offer to teach you to fight if you meet him at the docks, but only after you get him some Ale.

Make a quick trip back to the tavern and get a mug of ale from the bartender and take it to Lyle. When he is ready, go meet him at the docks for Combat Training. You will have to learn Defense, Striking, Dodging and finally beat Lyle in a full fight. Once you have successfully completed the training you can return to the tavern and talk to Captain Justice again. After some more conversation you will set sail and leave Lizard Point.