Mark diagonal lines on both ends of the pillars. The intersecting point is the center.
Drill pilot holes for 1/2-inch washer head screws centered on one end and pilot holes for 1-1/2-inch wood screws centered on the other end (image 1).
Use the center point on the platforms as a guide for marking the placement for the lazy Susan bearings. Center the 4-inch bearing on the 9-inch platform, the 6-inch bearing on the 12-inch platform, and the 12-inch bearing on the 15-inch platform. Mark the position of the screw holes and drill pilot holes for the 1/2-inch screws.
On the 1/2-inch pilot hole end of four pillars, position the opposite side of the 4-inch bearing from what was marked on the 9-inch platform to line up the screw holes, and attach using 1/2-inch screws (image 2).
Measure the width and depth of the outer edge of the pillars where they are attached to the bearing. Mark a square matching this dimension centered on the 12-inch platform. Position the pillars in this square, align them with the corners, and mark the outline of the pillars on the platform (image 3).