First, determine what kind of backers you need. If you are putting together a show for production at a profit, you will mostly likely need investors. If you are looking for funding for a theatrical company, you might need a patron. If you are looking to help out in your non-profit cause, you'd want to find a backer with ties to that cause.
Contact local theatrical companies to find out who their backers are. In most cases, they will be more than happy to talk to you. In the event that they are less than forthcoming, you can always get your hands on some old programs and look through it to find out who might be the "money people" behind the event. If you are looking for backers for your non-profit group, other theatrical groups might be willing to lend you assistance in your search.
Contact the people identified as possible backers. In most cases, the most effective way of raising money from a theatrical backers is to contact them by telephone. It is easier to find a backer for your production when you speak to them on the phone, rather than simply sending out a letter asking for funds.
After your initial phone call, send a follow up letter. Reference the phone call in the letter, and emphasize why you are contacting this specific individual. If you are looking to find a backer for a theatrical company, for example, explain that being a patron to the group will have benefits, both in terms of public relations and in terms of a philanthropic gesture.
Give a call to your local newspaper and explain that you are looking for theatrical backers. In many cases, they will do a small "human interest" piece on you and provide contact information that a potential backer can use. This approach is especially effective if you have a "non-profit" angle that can be used, generating even more of a "human interest" aspect.
You can also try to raise money for your project by going online. Using a simple program such as Squarespace to build a website, you can explain what it is that you're trying to do on the website and solicit funds. Then, do a web search for any theatrical backers that you have discovered and send them an email directing them to your website. If your production is linked to a specific cause (such as heart attack awareness), do a web search of organizations that have ties to your cause.