Based on your other thread, it appears that you're doing this on Sat night/Sun Morning. Either the Q33 or the M60 bus will be perfect.

Q33

From Manhattan, take an E, F or R train to the Jackson Heights/Roosevelt Avenue station. Go upstairs, out the turnstyles and straight out the door to where the buses pick up. Catch the Q33 bus at 4:00am, and you'll be at LGA about 20 minutes later.

M60

From Manhattan, take the N train to Astoria Boulevard. Exit the tunstyles and walk down on the side of the street where the traffic is coming off of the Triborough Bridge, rather than going onto the bridge. As you come down the stairs, you'll see a small plaza with a statute; the M60 bus stop to LGA is very close to that. There are buses at 3:53, 4:23 and 4:43. The trip will be about 15 minutes.