Florist clay is used for many different uses in a professional flower shop. Cling is a favorite brand of mine, since it comes on a roll separated by a paper tape rather than in a brick than can dry out over time.
You can pull off the length you need while the rest of the roll stays protected by the covering until needed.
Many florists use double faced tape or the newer Uglu adhesive to attach the flower stems to the bouquet handle. I like to use the floral clay because it secures firmly even wet flower stems, holding them exactly in place until I secure them with wire or BindIt tape.
Press the strip of florist clay at the very top of the bouquet holder handle.
Wind the clay tape gently down the stem. This will be sticky - yet not make a mess if you lightly touch it with your hands.
See how using the the florist tape on the handle conceals it under the clay.