I'm going to a wedding in August, but I'll be coming in from Winnipeg. What's the "best" way to get to the Stewart area? Is it fairly simple to fly to LGA and then shuttle or take the train up?

Fly to HPN.. Westchester County Airport and rent a car ... 1 hour closer than LGA

Norwegian runs a shuttle bus from Stewart to Manhattan, coordinated with their arrivals and departures. I don't know about the other carriers.

It is not simple and it will be long.

No you'll need a cab, Uber or rent a car.