Florists use either clear florist tape or waterproof tape (which I generally prefer because it holds better).
Clear tape is usually used with clear glassware because it becomes invisible to the eye. Just remember the glassware has to be dry for the tape to anchor firmly to the glassware. Waterproof tape holds better, but the designer has to take care to conceal it with flowers and greenery.
Here is my stack of foam pieces, secured into place with the wooden Cowee picks.
It's rather hard to see how I anchored the foam to the bottom glassware with the clear tape. You'll see red arrows pointing out where the clear anchor tape is wrapped around the foam.
This angle shows the tape, which I wound completely around and under the plate to ensure it stays in place. This is primarily so the piece stays firmly secured during transporting your flowers.