How does one become a floral designer?

At the local college where I live they offer classes in the continuing education department.

Work for a while at a florist (or even a greenhouse, though that is a LOT of hard work, longish hours and low pay). I worked for two years in a greenhouse and then another two years in a florists. After working with a florist for a while, you should be instructed on how to construct arrangements. If you already have a degree in design, then all the better, but it seems (from my quasi-outsider-insider perspective) to be a hard business to start up. I also second what gooch said about continuing ed.