Step 1: Tools and materials
The basic components of the project are:
2 16 inch wooden disks (the base and top shelf)
1 18 inch wooden disk (the bottom shelf)
1 6 inch lazy susan ball bearing assembly (500 lb rating)
3 ft 1x4 stock for 3 "pillars" to support the top shelf
3 ft 3/4 x 3/4 stock for the top cross-piece
3 ft 3/8 inch dowel
You should be able to find these parts at the local hardware store or home center. Some of them even sell pre-cut wooden disks in plywood or laminated pine. The plywood is strong, but the edges don't finish up that well. I cut my own disks out of some 3/4 inch laminated pine sheet, which was cheaper than getting pre-cut disks, and the rest of the stock is poplar.
A note on cutting disks: if you don't have some sort of circle cutting jig for a router or band saw, don't try to cut out circles. You'll bodge it up. Just make some octagons instead.
And a final note on the lazy susan: it might seem ridiculous to use a 500 lb rated turntable for a little desktop bookshelf, but they're not expensive, and the main criteria is that the base plates have screw holes that are large enough to hold some decent wood screws, and they are spaced widely enough that the screw heads won't collide when the plates rotate. Also, keep the hardware packed away, so it doesn't get dusty. Any grit or sawdust in the ball bearings will impede smooth rotation.