Cut dwarf sunflowers early in the morning before the sun has a chance to dry them. Cut the stems at an angle and remove the lower leaves that would otherwise be underwater in the vase.
Place the cut sunflowers in a container of water immediately. Place the container in a cool, shady location and allow the flowers to soak for several hours or overnight.
Recut the stems an inch or two above the first cut while holding them underwater. Use a sharp knife or pruners to make a vertical, 1-inch cut that splits the end of the stem.
Prepare the floral preservative according to the package instructions and fill the vase. Place the sunflowers in the vase.