I have a flight from Atlanta to New York (LaGuardia Airport) with Delta, and then another flight from New York (JFK) to New Delhi with Air India. Do I need to collect my check-in bags in New York and check-in again?
You will definitely need to collect your luggage at LaGuardia airport and transfer it and yourselves to JFK airport to check in for your next flight.
There are a number of shuttle services between these two airports that will take 45-60 minutes (plus the time to wait for the next one to depart). Alternatively taxis will take around 30 minutes depending on the time of day, which will cost around $40.