Consider flying into BOS, as it often has lower fares. It's closer to PVD than SEA is to YVR. If you don't want to rent a car, a short Silver Line ride on Boston's MBTA rapid transit system will take you from your arrival terminal to Boston's South Station, where you can get a train to Providence and points south, though I don't know how close it comes to East Greenwich. Amtrak will have the fares and schedules for that, so you can decide if the overall cost and schedule are worth it. There are also, I think, buses from BOS to Providence.

As others have posted, it would help if you could tell us what research you have done, what Web sites and other methods you have tried, what you have found, and what improvement you would hope to get. People here tend to be willing to help those who have taken some steps to help themselves first, but can get snarky toward those who haven't (or might have, but you can't tell from their posts).