May I ask please, rather than giving you some worthless information, are you by chance trying to get to Kennedy..or are you going beyond. If it's just to the LIRR, then there are shuttle services you can take from LGA. But if it's actualy in to JFK, there are some other options.
I need to leave now, so �just in case� I�ll give you some details that may be helpful. There are busses operated by Carey just outside of baggage claim. The journey time from LGA to Jamaica LIRR Station is about 30-45 minutes and coaches operate about every half hour up until around 2300.