You will not find a high street in Florence with all major top department stores etc. Instead, you will mostly find small shops selling souvenirs , antiques, furnishings, leather goods, clothing and shoe boutiques. Florence is also popular for its many outdoor markets.
Via dei Calzaiuoli running from the Duomo to Piazza della Signoria. This street is probably the main shopping street in central Florence.
Via Tornabuoni you will find all the big names in Italian fashion - Armani, Gucci, Versace, Coveri, Ferragamo...
San Lorenzo Market around Piazza di San Lorenzo, for handbags, leather jackets, belts, jewellery, gifts etc.