The put-in is pretty hairy, right below the dam in West Groton, but after you turn the first corner it's smooth paddling down this beautiful stretch of water. Surrounded by the Groton Town Forest, there are no signs of civilization in sight, except for some abandoned railroad tracks that run parallel for a couple short stretches.
Windy, narrow, and shallow describes the river itself; as remote as one can get in the middle of Massachusetts. The Squannacook flows through Shirley as it empties into the Nashua, about 2 hours paddling from the dam, if you don't take too long exploring the pond that comes off the Squannacook. After getting on the Nashua, you'll see three obvious signs of civilization before you're done for the day - Richard's Boat House, with large dock on the water (with an incredible set of trails through Groton Place behind it), used for Groton School's crew team; the cars over the bridge of route 225 a little below there; and the new bridge of route 119 right before the takeout. The takeout is about 2 or so hours downriver from confluence of the Squannacook and Nashua, at the Petapawag boat launch. All together, it's a splendid paddle through a whole lot of conservation land - a perfect way to relax.
Spring and early summer is the time to hit this route, since the Squannacook tends to be shallow at other times, and with the fallen trees and beaver dams, can require a few haul-overs, though no true portages, unless you're paranoid about scratching up the bottom of your boat.
Parking lot at the put-in, state forest/boat ramp at takeout. Free camping in the state forest, bed and breakfast nearby, Groton Inn in town.
Route 119 to Groton, turn off onto 225 and follow to the bridge right before the Groton/Shirley line. A small parking area is on a dirt path on the right directly after the bridge; put in below the dam, across the street.(119 is the Littleton exit off 495, head towards Groton)
For the takeout, follow 119 towards Pepperell, turn off onto Nod Road right before the bridge into Pepperell, look for the big brown sign that says Petapawag.