Take a shuttle. LaGuardia offers three shuttles between LGA and JFK airports; ETS Air Shuttle (718-221-5341), All County Express (914-381-4223) and New York Airport Service Express Bus (718-875-8200). Call to make a reservation with any shuttle service. Prices range from $12 to $33, and the travel time between LGA and JFK is generally between 45 and 60 minutes.
Hail a cab. A uniformed taxi dispatcher is located in ground transportation. She will arrange for a cab to pick you up immediately and transfer you between airports. According to the Port Authority's website (see References), the fee for a cab from LGA to JFK is between $25 and $29, but most often you will find that it's more than that, depending on traffic.
Book a van or limo with a private service. When you exit your plane, head to the ground transportation information center in baggage claim to book a van or limousine to transport you from LaGuardia to JFK. The price varies depending on the type of vehicle you choose to book.