Take a taxi. A YELLOW taxi. Not the from the guys that will all but jump on you in baggage claim at LGA saying "taxi?". Go to the taxi cue just outside baggage claim (it doesn't matter which airline you come in on). You can't miss the line of yellow cabs. To JFK will probably be about $25-30. Its fast (20 min), safe, direct and you won't have to worry about connecting with buses and the AirTrain.

Only possible other alternative is the direct bus fro LGA-JFK that will save you some money but cost you time.