I like to use the orchid to demonstrate this because the orchid is nice and hearty. It doesn't really need water in a floral arrangement. It can survive even for a few days without water. If you get at all concerned about the survival of the bloom, using wire, you can take (ta-da!) a nice water pick that you fill with water. It's got a rubbery top and you can actually feed the end of the bloom through the water pick and then cover it with the tape that we're going to use. Today we'll just use the wire and the tape.
Now, the floral tape is a lot of fun to work with because it's very stretchy and it's easy to manage. Pull out just a few inches of the floral tape. Holding your flower at the base, begin wrapping the flower stem and the wire. You just wrap like you would wrap an Ace bandage or anything else. Keep wrapping and wrapping. As you wrap, you want to pull a little bit taught and wrap. Pull a little bit taught and wrap. You can see that I'm starting to create a nice sturdy stem. This wire is going to help the flower not only stand up and stand tall, but it's also going to be malleable. I can bend it. So if I needed to angle the orchid bloom, I could do that. You wrap it all the way to the bottom.
Now, when you get to the bottom, just pull the tape. If I look and I feel like it's not quite thick enough, I could always do another round with the tape all the way down the stem. You can make this stem, because it's the stem you're creating, as thick as you'd like. When I'm all finished and I want to measure it for the floral arrangement, if it's too tall I can always clip it with my trusty clippers.
That's how you wire a flower for a floral arrangement.