This vase is built by using multiple rings of multiplex (plywood) boards glued on top of each other and then turned using a lathe.
Step 1: What you need
Some scrap multiplex boards which must be size of the maximum radius of your vase.
Any saw that can make round cuts (bandsaw, jigsaw or even a scroll saw).
A lathe (or a sander, but this will take very long!).
compass (for drawing circles)
Paper and pencil:-)