The easiest way is to take a taxi it's a flat rate from Lga to anywhere in NYC..
Get on the Q70 to Roosevelt and get on the E train
You're going to have to find a bus that'll take you to Jackson Hights Roosevelt Avenue, a subway station, and take the subway (this includes some transfers) to battery park, where the ferry is to the statue of liberty. I don't know the specifics on what busses or subways but that's the basic directions.
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