Lay the 15-inch square on the workspace. Extend the measuring tape from one side to an opposite side. Make a mark at 7½ inches. Using the mark, place the measuring tape across the square at a right angle to the sides you used previously. Measure and mark at 7½ inches. This is your center point. Drill a hole the size of the screw end of the spindles.
Coat the inside of the hole with wood glue. Apply the first spindle, screw side down, into the hole and screw into place. Allow the wood glue to dry as you cut the next pieces.
Use the 8-inch squares in the next level. At one side, measure 2 inches from the corners in both directions. Use the measuring tape as a guide and draw a line from one mark of a corner to the other mark of the same corner, giving you a triangle. Cut these corners off with the saw. Sand down the edges. Drill a hole at the short end (where the corners were cut) in the middle and an inch in from the edge. Do this for each 8-inch square.
Screw one of the spindles into the top of the shaft set into the base. Screw another shaft into the top of the spindle. Put the hole of each 8-inch board over the shaft and slide it down. Screw a spindle in over the top of these boards; don't tighten to the point where the boards can't move, they need this to be adjustable. Screw another shaft into this spindle.
Using the 6-inch squares, repeat the procedure for making the plant holders in Step 3. This will give you the second level in the tier. Continue by applying these pieces to the stand as you did the 8-inch pieces in the step above.
Do the same procedure with the 4-inch squares next. This will create the top level of the tier. Screw in the end cap to finish the plant stand.