Or take public transportation:

Step 1:

Take a train to New Haven (Union Station). Both MetroNorth and Amtrak have frequent service. Or you can get there via Greyhound bus. An information kiosk is on your left as you enter the main waiting room. There you can obtain maps, schedules and tokens. You can get a taxicab outside the station to take you directly to the museum. The fare is approximately $10. OR, you may complete your trip by bus:

Step 2A:

Take a Connecticut Transit bus directly outside the station, route A, J or JU. Be sure to ask your driver for a free transfer when you pay your fare of $1.25 (coins, dollar bills or tokens are accepted). Take the bus to Church and Center Street. Walk one block further along Church Street, turning right onto Chapel Street, then proceed to the F bus shelter in the middle of the block. OR:

Step 2B:

You can save one bus if you don't mind walking an extra 6 blocks. When you exit the train station, turn right. Walk along Union Avenue. You will walk under the Route 34 elevated highway structure and emerge on State Street. Continue northerly along State Street to Chapel Street and turn left on Chapel Street. The F bus stop is on Chapel street at the southwest corner of Chapel and State.

Step 3:

On Saturdays, F buses depart every half-hour at :10 and :40 after the hour from downtown New Haven. On Sundays, the F is combined with the G and is called the GF. Buses depart downtown New Haven every hour on the hour. Weekday service is more frequent.

Step 4:

Take the F bus into East Haven. Different buses stop at slightly different locations. Tell your driver that you want to go to River Street, by the East Haven Green. It will be at most 3 blocks from the bus stop. Refer to the East Haven street map above. Once at the Green, walk down River Street 3 blocks to the end of the street, where you will find the museum.

Step 5, Returning to New Haven:

The bus stop is at Thompson and Main. From the museum, walk up River Street 3 blocks till it ends at Hemingway Avenue. Turn right, walk one block to Main Street (Route 100) then cross Hemingway Avenue. Walk up Main Street 2 blocks to Thompson Avenue. The bus stop is opposite Metcalf drugs. On Saturdays, buses return to New Haven every half hour at :14 and :44 past the hour. On Sundays, buses operate every hour at :32 after the hour. The Sunday bus stop is River Street and Hemingway Avenue. The last bus is at 5:44 PM. Be sure to ask your driver for a free transfer when you pay your fare.

Step 6:

Take the bus from East Haven back to New Haven, getting off on Chapel between Church and Temple Streets, New Haven Green. Walk up to Temple Street, turn right and walk to the bus stop about 2/3 up the block (between the Center Church and the United Church). Take a J or JU bus back to Union Station, OR, for 1 less bus and 6 more blocks, get off 1 block earlier at State Street. Walk down State street, towards the elevated highway structure. You will pass Crown Street and George Street. If you pass Court Street you are walking the wrong way. Go under the highway and you emerge on Union Avenue. Continue walking a few more blocks along Union Avenue until you reach the train station.