There are a few ways of getting to Foxwoods from the NYC metropolitan area (NJ, CT, NY) and most people will arrive by car. It's the easiest and fastest way of getting to the casino in my opinion, although some people will arrive in day tour buses.
Our route to Foxwoods usually takes us about 2.5 hours driving East on I-287 to North I-95 to exit 92. After exiting you will stay to your left and follow the signs, about 10 miles on this road before you get a glimpse of the massive casino ahead of you.
Since this was a spur of the moment trip; we drove. We were already on I-95 in Connecticut so we kept heading North. We got off at exit 92 and then followed the signs to Foxwoods. It was about 8 miles from the Highway to the Casino.
I-95 is always a fast drive and unless there is an accident, holiday or rush hour; the traffic isn't bad.