The best potential clients are those who already use copywriters. They're knowledgeable, they know what a copywriter can do for their business, and this makes them easier to work with. But how do you find these gems?
The fastest way is on the Web, no sleuthing skills needed. Do a search for advertising, multimedia, and PR agencies in your city or state on Google. Many agencies publish their client lists. Then go ahead and contact these businesses and introduce yourself and your services.
A copywriter friend to whom I recommended this method asked: "Isn’t this unethical?"
If you're not a sub-contractor with a particular agency, then no, it's not.
Even if you are a sub-contractor for an agency, it's still not unethical if you let the agency know what you're doing. A business will have many business writing needs which aren’t handled by the agency. For example, an advertising agency might do all a business's advertising work, but the business will still need other marketing communications material.
If you have done work for an agency client, be completely honest and open and tell the agency that you're going to approach the client and ask for other work --- before you contact the client.
Usually, the agency will prefer that you don’t mention that you're a sub-contractor; they like to give the impression that they do all work in-house.