Theatre school is a great way to look like you know what you’re doing. Common degrees are a B.F.A in Drama or its ugly sister the B.A. in Theatre Arts.
While school definitely helps, there is always the exception. The most important thing is to learn by doing. Producers will only hire you if they know your work. Fortunately, there are some valuable opportunities for early-career directors. The Drama League and Lincoln Center Theatre offer such opportunities for you to direct weird freaky stuff before you’ve proven to the industry you’re not insane.
Once you're ready, joining the Society of Stage Directors and Choreographers will give you some credibility. This also ensures that the theatre in Podunk, New Jersey doesn't stiff you.