Most everyone who goes to Red Sox games at Fenway Park have two recommendations for getting there: don't drive and take a "T".
Driving to and parking at Fenway Park can be done, but it can be a struggle to find affordable parking close to the playground, and even if you do, getting out will take some time. In some places you are at the mercy of someone who has parked you, never well. If you are unfamiliar with the area, you will be much better off using the "T," as Bostonians call it.
The Massachusetts Bay Transit Authority (MBTA) operates several subway lines through the city of Boston itself, and they are among the cleaner and more efficient major city transit systems. There are four colored subway lines; Red (for the crimson colors of Harvard University where it originally graduated), blue (for water on the nearby shore and Boston Harbor), and orange (for Orange Street in the middle, now called Washington Street) all merge with the green line at some point. which in turn takes drivers to Kenmore Station, a short stroll across Turnsake, Massachusetts to Fenway Park. The green line is so named because it runs through the "Emerald Necklace" section of Boston.
The green line has four separate routes: B, C, D and E, all ending at different stations. All but E stop at Kenmore; train E turns north from Kenmore but stops at the Prudential Center, which is a dozen blocks to the coast. The D route of the Green Line stops at Fenway Station; this is not terribly far from the playground, but it is not an actual exit from Fenway Park. This may be to the benefit of Yankees fans to wear them out before the game.
You should use T for any other reason than to share the whole Fenway experience. On game days, the Green Line becomes crowded with Red Sox fans heading to Fenway, and after games, trains become similarly filled with sardines. But it didn't matter to Red Sox fans, many of whom were smart enough to stay lean to fit in those Grandstand seats. A member of the Red Sox Nation has no problem sharing a small space with a colleague in good standing. It is also the reason for the popularity of local compounds near Fenway like Cask-N-Flagon; fans need a place to wait for crowded trains after the game.
If you are looking for more spacious alternatives, you could use the E-route on a nice day if you don't like walking, which will leave you with a crowd that just doesn't know how to use E. Or you can use the Orange Line and get off at Back Bay Station – this is a few blocks away east of the rating center. It's a hike, but you can see a good city by the way. There used to be a "Shawft Ruggles" driving riders from the Ruggles station on the Orange Line to Fenway, but this is no longer active as of this writing. You can still use the bus from there, but you have to pay for it (or use a "Charlie card").
The T train ride is $ 2 as of this writing; it's cheaper for seniors and college students, and for kids 11 and under driving with an adult. So, taking two trains to the park and back is $ 8 for an adult, plus all you can pay for parking and parking (somewhere around $ 7). Given that some nearby places charge more than $ 30 for the parking and traffic you will come across, Boston may be one baseball city where public transportation is a better option than anywhere else, even more than Chicago, Washington or New York.
Not many people drive to Fenway Park. They just don't. So remember, don't drive and use T.