One Suggestion: Fly into LaGuardia, take the M61 Bus from outside of baggage claim, and get off at 125th street and Park Avenue at the Metro North Station. From here, you can get the train to Valhalla.
Otherwise, you can do the same thing, but get off at 125th Street and Lexington Avenue, take the 6 (subway) to Grand Central Station and take Metro North from there. The only benefit is that if you have to wait for your train, you'll have a nicer place to wait, but the trains run pretty regularly, so you probably wouldn't have to wait too long.
If you take a cab from LaGuardia, ask for the cab driver to drop you off at MetroNorth's 125th Street Station (125th and Park). If you take a cab from JFK or Newark, ask the driver to bring you to Grand Central. I would recommend option number one, first - the bus is 2 dollars and can be paid on board. If you feel intimidated, though, just take a cab. What's an extra 30 / 40 bucks at this point, right? 🙂