Most everyone who goes to Red Sox games at Fenway Park has two recommendations on getting there: do not drive, and take the "T".
Driving to and parking at Fenway Park can be done, but it can be a struggle to find affordable parking close to the ballpark, and even if you do, getting out will take some time. In some places you're at the mercy of someone who has parked you in, never a good thing. Unless you're familiar with the area, you're much better off using the "T", as Bostonians refer to it.
The Massachusetts Bay Transit Authority (MBTA) operates several subway lines across the city of Boston proper, and they are among the cleaner and more efficient of big city transit systems. There are four color-coded subway lines; Red (for the crimson colors of Harvard University where it originally ended), Blue (for the water on the nearby shoreline and Boston Harbor), and Orange (for Orange Street at the middle, now called Washington Street) all connect with the Green Line at some point, which in turn takes riders to the Kenmore Station, a short stroll over the Massachusetts Turnpike to Fenway Park. The Green Line is so named because it passes through the "Emerald Necklace" section of Boston.
The Green Line has four separate routes: B, C, D and E, all of which end at different stations. All but E stop at Kenmore; the E train veers off north of Kenmore but stops at the Prudential Center, which is about a ten block walk to the ballpark. The D route of the Green Line stops at a "Fenway" Station; This is not significantly far from the ballpark but is not the actual Fenway Park exit. This may be for the benefit of Yankees fans, to wear them out before the game.
You should use the T for no other reason to share the whole Fenway experience. On game days the Green Line becomes packed with Red Sox fans heading to Fenway, and after games trains becomes similarly sardine-packed. But this is of no nevermind to Red Sox fans, many of what were smart enough to stay slim in order to fit in those Grandstand seats. A member of Red Sox Nation has no problem sharing a small space with a fellow member in good standing. This is also a reason for the popularity of local joints near Fenway like Cask-N-Flagon; fans need a place to wait out the post-game train crowds.
If you're looking for more spacious alternatives, you could use the E route on a nice day if you do not mind the walk, which would keep you out of the standing room only crowd that only knows to not use the E. Or you could use the Orange Line and get off at the Back Bay Station-this is a few blocks east of the Prudential Center. That one's a hike, but you can get a good look at a beautiful city along the way. There used to be a "Ruggles Shuttle" that took riders from the Ruggles Station on the Orange Line to Fenway, but that is no longer active as of this writing. You can still use a bus from there but you have to pay for it (or use a "Charlie Card").
A ride on a T train is $ 2 as of this writing; it's cheaper for seniors and students and free for children 11 and under riding with an adult. So a two-train ride to the park and back is $ 8 for an adult, plus whatever you may pay for a park-and-ride lot (somewhere around $ 7). Considering that some nearby places charge upwards of $ 30 for parking and the traffic you will encounter, Boston may be the one baseball city where public transportation is a better option than anywhere else, even more so than Chicago, Washington or New York.
Not many folks drive to Fenway Park. They just do not. So remember, do not drive and use the T.