First, you need to have completed the Monkey Island Mix recipe.
More about the recipe...
Then, you need to let Guybrush know you've reached Monkey Island.
Bring him up on deck.
Now, how can you get to Monkey Island?
The solution lies nearby.
Remember the Fettuccini Brothers?
Maybe you could fire yourself from the cannon to Monkey Island.
For the cannon to work, you'll need to load it and light it.
How can I load the cannon?
How can I light the cannon?
But Guybrush, of course, also believes in safety.
He'll need a helmet.
Where dcan I get a helmet?
Once you have loaded the cannon, obtained a helmet, attached a fuse to the cannon, and have the flaming mass, use the helmet by the cannon, and you'll automatically fire yourself onto Monkey Island.