Cap'n Salty will give you the jet ski keys (and a lobster) if you recover his lost lobster trap.
You have to dive using Scuba gear, which you can get from the owner of the camera shop. Catch the old photo floating in the wind next to the left side of the lighthouse, and bring it to the Say Cheese shop. Put on the gear and find the trap at the bottom of the bay. Cap'n salty will give you a lobster and the jet ski keys.
To use the jet ski, climb the lighthouse and look thru the telescope. You will see a small island with two seals, and a rolled up paper underneath. Race Nate on the jet skis to get it.
You go to the harbour and click on the jet skies. after that you will compete with Nate to the island with the map.
You don't just get the keys after you get the lobster and the scuba gear then the guy that wants it will give you the keys.
You do not play as Big Nate. He accompanies you around most of the island, and races you on the jet skis.
Look through the telescope on top of the lighthouse to see where you are going : the seal rock has a map under it. Race Nate to the island to get the map.
You have to look through the telescope on top of the lighthouse to see where you are racing to, which is the island with the seals and the seesaw rock.
If you wait for him to finish, you get both. If you left early, check your item bag for the keys.
You don't use the boat on Big Nate island. When you have recovered Cap'n Salty's lost lobster trap, he will give you the keys to his jet ski. Look through the telescope atop the lighthouse to see where you are headed. You also have to outrace Nate.
The key fits the jet ski, so you can race Nate out to the seal island to the right of the lighthouse (you can see it through the telescope). The map to the time capsule location is there. (see related question)
You don't. Give the trap to the old man (Cap'n Salty) and he will give you a lobster and the keys to his jet ski.
It is on top of the lighthouse. You can see Seal Island from there. But you can't go there until you recover the lobster trap for Cap'n Salty, who will give you the keys to his Jet Skis.
Tilt the rock by moving the seals to the left side. You can now retrieve the paper, which is a map to the Time Capsule on Big Nate island.
First you need the keys to the ski jet. Go up the lighthouse to the painter and ask him to see through his telescope. Look through and use your mouse to go right and up. You will see a paper wedged between a rock. Go down and click on the ski jet. Nate will run up to you and you start racing.