The best way to get to the game from Boston is by train, but it doesn't get there very early and leaves right after the game.
If you drive there and go into the regular parking lot, it will be a zoo when you leave. From Boston take 93 south, to 95 south to route 1 Foxboro.
If you would rather get there early and don't mind spending a little more, there's a tailgate party across the street. I used it last year with my son and we had a blast. The eight drink tickets each helped. It was also much better to get in and out of as we had our own travel lane separate from the parking lot traffic. This is the link.
All-Pro Celebrity Tailgate Party
Have a great time whatever you choose.