Qualifications
There are no national requirements to becoming a wedding planner. Because there are over 10,000 wedding planners in the United States, some people get a leg up on their competition by becoming certified. Certification requirements and course lengths vary depending on the career school you choose. Some career schools offer certification after one day, while others take up to six months. (The six month ones cost a bit more, but are significantly more thorough, as you might imagine.)
A number of wedding planners join the Association of Bridal Consultants (source). By joining the association, you're able to gain training, career support, liability insurance, and attend annual conferences. Before you hang a "Wedding Planner" sign over your front door, you need to have a business license. Business licenses are obtained through local agencies.
Okay, so you have a business license and you're ready to plan weddings. It's still not that easy. You need to market yourself to find clients. Early on, you may need to slash your fees to get experience and a portfolio, and to make some business relationships. When you use the same vendors for wedding after wedding, they start to recommend you to clients.
Your weddings must come off without a hitch. Remember, florists, bakers, venues, and caterers put their names on their products. A wedding disaster makes their businesses look bad.