Angle cut one end for the miter and begin easing the molding on to the base. I don't think this would work cold.
Ease one side of the molding on the base and push over to snap in place. I recommend pushing back towards the starting point as you go in case some shrinkage occurs in cold weather.
Cut your miters carefully 1/8-1/4" long. Push back to fit and it will expand hard into the 90 joint.