The fastest routing is rather complicated: I-84 through Hartford, picking up the limited-access highway CT-2 in East Hartford all the way to Norwich, then I-395 east for a few miles until you get to state roads CT-138 and RI-138 which lead you to I-95 just west of Kingston RI.

I-80 to I-95 seems to be simpler. But heaven help you if you are anywhere within commuting range of New York during the unpredictably long rush hours.

By the way, you cannot easily get from I-395 back onto westbound CT-2 (return trip) because for some reason CTDOT never built that ramp.