You will need the patience of a saint, as family law is one of the most frustrating things an attorney can practice.
Family law attorneys only need a law degree, which is a Juris Doctor. You need a bachelors degree to get into law school, so it generally will take seven years total: 4 for the bachelor's, 3 for law school.
After you graduate, you take the bar exam. When you pass, you become licensed as an attorney. Then you can go to work.
You can go to work for yourself, or join a firm. Fresh out of school, don't expect to make a lot of money. Family law can pay well, but generally people getting divorced are pretty much broke. Statistics state that a large percentage of people who get divorced then go bankrupt shortly thereafter. In today's economy, the housing market crash has caused most of my divorce clients to be under water - and even if they aren't, they still don't have any money just sitting around to throw at me. Most of them are like doing pro bono (unpaid) work.
If you get lucky, you might go to work for a high end firm in a big city that specializes in rich people's divorces - some firms in Chicago charge $50,000 just to walk in the door and talk to someone. But there are only so many CEO's of major corporations and professional athletes who can afford this. Most divorces are a losing proposition.