Research the laws in your state. Most states require licensing; a few don't. Virginia, for example, doesn't require licensing but does rigidly restrict who can become a settlement agent. According to the Virginia State Bar, Virginia "authorizes licensed Virginia attorneys, title insurance companies and agents, real estate brokers and financial institutions (or a subsidiary or affiliate thereof), to serve as Settlement Agents and provide 'escrow, closing or settlement services' if they register with the Virginia State Bar and meet other conditions of their regulatory agencies."
Visit a local real estate, title or escrow company in your area and talk to people in the business. Ask them what their companies require of settlement agents and how you might go about becoming an agent.
Complete the educational requirements of the state in which you live, if there are any.
Acquire a real estate license. Regardless of whether you ever plan on selling a house or other property, get your real estate license as a prelude to becoming a settlement agent. Most states require it, and most companies insist on it. Regardless of your decision, knowledge of real estate laws and practices in your state will prove invaluable. Mortgage Daily News is a clearing house for real estate news and information, including licensing requirements for all 50 states and Washington, D.C. In most cases, you'll have to file an application with your state to take the real estate exam, and then complete and pass it. Fees are involved.
Get a job with a real estate company. You can do this even before you get a real estate license. You can work in a real estate office and answer phones and do paperwork--although, obviously, you can't sell real estate. Once you've received your real estate license, you may or may not actually want to get into the buying and selling of houses, but you'll have gained experience that will go a long way towards making you an attractive candidate for a settlement agent position.
Apply at a company---real estate, title, escrow---for a settlement agent position. Don't be averse to accepting initially a position other than that of a settlement agent to get your "foot in the door."