From ChatGPT…

To take public transportation from Boston Logan Airport to Hampton Beach, you can follow these steps:

Take the free Massport Shuttle Bus from the airport to the MBTA Blue Line Subway Station. Follow the signs for the "MBTA Subway" or "Airport Subway Station." Take the MBTA Blue Line Subway from the airport station to the Bowdoin station. Transfer to the MBTA Orange Line Subway at the Bowdoin station, and take the Orange Line to North Station. At North Station, transfer to the Newburyport/Rockport Commuter Rail Line and take the train to Newburyport. At Newburyport, transfer to the C&J Bus Lines bus service to Hampton Beach. You can check the schedules and fares for the MBTA and C&J Bus Lines online to plan your trip in advance. It's also a good idea to have cash or a credit/debit card to purchase tickets for the subway and bus rides.