That's the big question. Some folks say to start today, others say to start tomorrow. If you start today, March 10, you will be finished your novena on the Eve of the Feast of St. Joseph. That, I believe, is the more traditional procedure. Start tomorrow and finish on the actual Feast Day. Really, I don't think St. Joseph minds either way!
Once you've decided when to start, jumpstart your novena at aeternus with some words from Saint Teresa of Avila and a beautiful image of St. Joseph: Devotion to St. Joseph.