There are basically five things to cover in this type of business introduction letter (each can be a separate paragraph):
1. State your reason for writing (i.e., to introduce yourself and your business).
2. Provide your name, title/position, and a "tag" to help cement your business' market position in the mind of the customer (for instance, "the low fee provider of medical staffing service" or "the most experienced medical staffing service provider in the tri-state area" or "the only locally-owned staffing service provider" or . . . you get the idea).
3. Give the recipient a brief (yet persuasive and undeniable) reason to contact you
now (for instance, if your recipient is a job seeker, it might be something like, "I have a wide range of openings to maximize your opportunities" -- or if your recipient is a health care facility, it might be, "I may have that one special person you are looking for to complete your existing staff." If you're offering any introductory discounts or other incentives, this would be the place to mention those, as well.
4. Invite action -- ask the recipient to call you now, to discuss something specific, to make an appointment, or whatever action is desired. The important thing is that you don't just say, "Here am I!" and leave it at that (a common mistake with introduction letters and new business announcements). Compel the reader to DO something -- right then -- rather than set the letter aside and forget about it.
5. Express your appreciation for the recipient's time and consideration, and end with a positive expectation (such as, "I look forward to helping you fulfill . . .")
This format assumes that you have a somewhat "qualified" mailing list -- i.e., the reader will recognize what it is you do, and be at least prospectively in the market for your services.
Welcome to the community and good luck!