Round planters are less difficult than they look once you crack the problem of making the staves. The first trick is to use a large number of vertical staves; technically this makes a multisided polygon, but it looks round. The second trick is to angle the edges of the staves so the inside width is slightly less than the outside width; this makes them butt together to form the circle. The correct edge angle differs with the number of staves. Using 24 staves, you can make a 19-inch diameter, 15-inch-high planter.
Cut the cedar boards into staves 15 inches long, making 24 staves in total.
Put a 7.5 degree bevel along both sides of each stave, facing inward so each stave becomes slightly wedge-shaped. Using the table saw, tilt the head 7.5 degrees and run the staves through flat. The width of one side remains unchanged, the other becomes slightly smaller. An alternative method is to rout the staves with a shallow chamfer router bit.
Optional: Using a router, put a 1/4-inch bullnose on one edge of each stave, and rout out a 1/4-inch bowl on the other side. (This reduces stave size to 2 1/4 inches wide, making the final planter an 18-inch diameter.)
Cut slots on the outside (wider) faces for the metal strapping. You need two slots 9/16 inch wide by 1/8 inch deep, located 2 inches from each end. Set the dado blade and run all the staves through the table saw, flipping them around for the second slot. Alternatively use a rebating bit on your router. Cut a similar slot on the inside faces for the bottom board to sit in. Put it 1 inch up from the bottom, and 1/8 inch deep.
Check your work after making a couple of staves! Fit them together then stand them up on the bottom board and check if the diameter of the finished planter is good. Check the strapping and bottom board will fit in the slots. Sand the top edges of the staves. Optionally you can round off the tops to help water run off.
Stand all the staves upright and check they fit together correctly. To keep them upright temporarily, fix a tie-down strap or rope around them. Measure the inside diameter of the planter. Using the jigsaw, cut the bottom board into a circle ¼-inch wider than your inside diameter measurement. This should be 17 3/4 inches for the standard version, 16 3/4 inches if you did bullnoses. Drill three ½ inch holes to allow water drainage.
Gluing the staves together is optional if you routed a bullnose. If gluing, apply wood glue to the edges of each stave; you need to work fairly fast to prevent the glue from drying out. Assemble the staves around the bottom board, making sure it fits into the inside slot. Clamp them together again. If you have a brad nailer, put a brad through each stave into the bottom board, using 1- or 1 1/4-inch brads.
Install the metal strapping. If using a strapping gun, install before the glue sets, and it will act as a clamp while the glue sets. If you are substituting plumber's tape, use the tie-down to clamp the pieces together for 30 minutes while the glue sets up before fixing the metal tape in place with wood screws through the punched holes.
Apply polyurethane or other exterior wood protection.
Drawing a stave template is helpful. The more exactly similar you make the staves, the better the planter will look. Make jigs or use a fence to line up staves for operations on multiple staves at once. If using plumber's metal tape, get wood screws with a head size to match the punched hole size. Routing a bullnose tongue-and-groove is optional; it makes the staves fit together more tightly. For router aficionados, there are glue bits that create V-slots instead of bullnoses. The formula for edge angles is 360 / # of staves / 2.
It is very easy to get stave edge angles wrong -- the most common mistake with round planters. The slots for the metal straps and the bottom board need to line up accurately.