Measure the widest part of the planter to determine the width of the plant stand. Cut two dowels to that length. One dowel will remain intact, and you will be taking out the center of the second dowel. Make an X with the two dowels by setting one on top of the other. Make sure the top dowel is centered, then use a pencil to mark where your two cuts will be made. After cutting, you should be left with two equal-sized dowels and an approximately 1x1-inch cube (which you can discard).
Clamp a scrap dowel to the intact platform piece you are drilling into, which will help secure the platform piece. Clamp scrap dowel to table. Mark the center of the length platform piece and drill a 1/4-inch wide hole into the piece. Repeat on the opposite side of the platform piece.
Measure half of a dowel pin and tape off drill bit to measure how deep to drill. Then drill a hole into both ends of the two smaller platform pieces where they will meet up with the longer platform pieces to form an X. You will drill a hole in the center of the four points of the X where they will connect to the legs later.
Apply a dab of wood glue to two dowel pins and insert them into either side of the center hole. Attach the other pieces to form your X platform, which will have pins sticking out of each of the four ends.
After determining the height of where the platform will connect to the legs (this will vary depending on your planter), mark a dot on the legs where your platform will connect. Drill a 3/4-inch deep hole into each of the legs at the determined height. Use wood glue and dowel pins to connect the legs to your X platform.
Let the wood glue dry for a few hours before sanding and staining. After the stain is completely dry, set a potted plant into the stand and place somewhere that fits the lighting needs of the plant.