Start with a cardboard egg carton. I used a combo of a craft knife and scissors to do all of my cutting. Cut leaves from the bent edges of the lid, as shown below. The flowers are obviously the cups of the carton; cut them out roughly from the carton, then shape the petals. Cut a few of the sticky-uppy posts for flower centers, too.
For the stems, I used 22-gauge cloth-wrapped stem wire, because I had it on hand. Pipe cleaners would have worked, but I'm all out of green ones! The 22 gauge wire was almost too stiff to work easily. I'd go down to a 24 or even a 26 gauge. (The weird thing about wire is that the higher the number, the thinner the wire.)
Anyway. Cut your wire into roughly 6 or 8-inch lengths. (I cut my 18-inch-long stems in half, and they were too long; I could have cut them into thirds and have been fine.) Poke a hole near one end of each leaf. Use a push pin and wiggle it around to widen the hole so it's big enough to slide onto the wire.
Anyway, here's how I made the flowers with hot glue. Substitute tacky for hot glue as you prefer; you'll just need to hold things longer (or lay them in place as the glue sets). First glue any inner blossom (made with an upright post from the carton) to its outer counterpart. Turn the flower over, dab a blob of glue on the middle of the flat part, and press the circle end of the wire into the glue, like you're an old-timey cowboy branding a horse. Hold as the glue sets. Slide a leaf onto the stem wire, and dab glue around and in the hole to secure it in place. All of this will be hidden so it's ok if it looks a bit messy.