ninerdriver

If you're lucky enough to line up with it, take the shuttle. It takes about an hour, and it's free unless you tip [insert fight about tipping here]. More realistically, the shuttle won't cut it, because the shuttle schedule sucks.

Here's the MTA way. It takes about an hour and fifteen minutes, and it costs $7.75. I do this regularly, and it hasn't failed me yet.

1. Take the red AirTrain to Jamaica Station (the train isn't red, but the sign is). Get or refill your MetroCard at the exit. It costs $5 to exit.
2. Follow the signs to the subway. You'll cross the LIRR tracks and take the elevator all the way to the bottom. Take a Manhattan-bound E-train toward the World Trade Center. Pay $2.75 when you enter. Get off the train at Jackson Heights/Roosevelt Avenue.
3. Follow the signs to the Q70 LaGuardia Link upstairs. The Q70 LaGuardia-bound bus stand is the third one out from the doors. Get a ticket from the machine at the bus stand. The ticket is free if you rode the subway to get there. If you don't see the ticket machines, then you're waiting in the wrong spot.