Spray paint the smaller four balls blue and the larger one yellow. Cut one end off each of the Styrofoam balls so that it has a flat surface to rest on, instead of being a true sphere.
Run a skewer into the opposite end of each of the four smaller balls. However, the skewer shouldn't enter at the exact opposite -- it should enter at an angle. Make sure that it's the same angle for all four balls.
Use the Sharpie to draw an equator around all four of the smaller balls. The "equator" should be perpendicular to the line that the skewer makes through the ball.
Attach the large yellow ball to the center of the lazy Susan with glue. Then attach the four smaller balls to the edge of the lazy Susan, on all four sides, directly opposite one another. Make sure that the skewer is pointing in the same direction for all four balls. They should not point in the same direction around the edge of the circle; when you look at them while the lazy Susan is stationary, they should all point in the same direction, because the Earth's axis doesn't change direction either -- it always points towards Polaris (for now -- in a few millennia, it will point toward Vega, but the drift is infinitesimally slow).
Label the four index cards "Spring," "Summer, " "Autumn" and "Winter." Put "Summer" on the table next to the ball whose axis is pointing right at the Sun. Put "Winter" next to the ball across the lazy Susan from "Summer." Put "Autumn" and "Spring" next to the other two. Turn the lazy Susan so that the "Summer" ball moves towards "Autumn," and you'll be replicating the movement through the seasons.