If you have a car, drive. I usually take the Mass Pike (Interstate 90) west from the Cambridge/Allston interchange to Weston, where I pick up I-95 south and follow it all the way to Providence. If you are in eastern Cambridge, get onto I-93 south near the Museum of Science, and join up with I-95 south of Boston. If you are in the Alewife area, I might consider taking Route 2 out to Lexington and getting on I-95 south there. Just follow whatever directions Google maps gives you to avoid traffic.
By train, its pretty easy to take the Red Line subway from Cambridge to South Station, and then catch either Amtrak or the MBTA Providence commuter line. I have found that Amtrak has a slightly better schedule if you are going down to Providence for the day, but it is also more expensive than the MBTA train. In Providence, the train station is an easy walk to things like the Brown and RISD campuses and most of downtown.