In need of a burglar-alarm system, a Washington couple pondered that inevitable homeowner's question: Out of all those home-improvement firms listed in the Yellow Pages, who will do the best job?

In this case, they phoned the downtown office of the National Burglar and Fire Alarm Association, which provided them the essentials to make a choice: a local list of established firms, an informational guide on types of alarms on the market and tips on how to conduct their search. Following this advice, the couple invited four alarm companies to survey their home, make installation recommendations and give a cost estimate. (People often get only one estimate because they hate to have to turn down the losers. But that's the way business is done.) After checking customer references, the two homeowners felt confident they were making a well-informed decision. At it turned out, the installation proved as satisfactory as they had anticipated.

Finding an expert to do a job right, as this couple discovered, is no easy task. It requires time-consuming research and questioning and maybe a touch of intuition. Even then, sometimes the most highly qualified person isn't the right one for you. Take, for example, the wish to hire a financial adviser to put you on the golden road to wealth. The natural choice would be a professional who is making a bundle for his or her clients. You check around with friends, business associates and your lawyer, and they come up with a name.

The adviser is legitimate, and money is rolling in. But this expert likes clients who are willing to take a financial risk, to gamble a little to make more in return. You, on the other hand, are the cautious type who prefers the steady growth of a sure thing to the real possibility of loss. Better find yourself a more-restrained expert who is closer in tune with your personality.

Say you are program chairman for your group lining up a speaker. Consider -- before getting the scientist with the most impressive credentials -- how well that person projects in front of an audience. Some of the big brains turn out to be duds on the platform.

Big companies know how to find the experts. They hire an executive search firm -- the experts at finding experts. Or they zero in on the federal government, the breeding ground for much of the regulatory legislation these corporations are always trying to work around. One national accounting firm, with big oil clients nursing tax grievances with Uncle Sam, recently sniffed out a young Washington lawyer in an energy-regulatory agency who had started his career with the IRS. Just the man with the rare combination of talents to counsel these clients. And so they whisked him west, not surprisingly with a healthy pay raise.

The individual, however, must seek out experts in less grandiose ways, usually trying to balance the degree of skill desired with how much the budget can afford. Top talent can cost.

How do you go about it?Each situation varies, but there are general rules that will head you in the right direction:

Ask for references and check them out. If your roof needs repairing, your best bet is to find someone you trust who recently has had work done by a firm that completed the job quickly, well and at a fair price. Don't forget to phone the Better Business Bureau (393-8000) or your community's consumer affairs office to ask about reported complaints.

Examine credentials. To sharpen their skills, many experts enroll in rigorous courses certified by their profession. The American Society of Plastic and Reconstructive Surgeons provides that kind of special training for plastic surgeons. Even your insurance agent can tack such letters as CPCU or CLU after his or her name, indicating adherence to the industry's ethical standards and completion of a series of qualifying exams.

Find out how your expert rates with colleagues. A lawyer active in a professional association and holding an office usually enjoys the esteem of the people who are looking most closely at his or her work standards. No association wants a loser as its representative. The public library can direct you to the Encyclopedia of Associations for the names and addresses of professional associations throughout the United States.

Ask for help. If you don't know where to start in finding a specialist for medical or mental problems, phone one of the medical or mental health societies for a list of names. (For a physician, call the Medical Society of the District of Columbia, 223-6333; Alexandria, 751-4611; Arlington, 528-0888; Fairfax County, 532-0500; Prince George's County, 779-0179; Montgomery County, 949-9497.) Physicians at major teaching hospitals tend to be up-to-date on medical techniques.

Seek out someone who can empathize. For personal concerns, there's nothing like a sympathetic -- and knowledgeable -- ear.That's the basis of such groups as Alcoholics Anonymous (966-9115) and Gamblers Anonymous (585-2151), whose members are experienced survivors helping those still struggling with the same problems. Career counselor Irene B. Ansher of Bethesda, whose clients include long-term disabled workers, figures she's more understanding of them because of a back injury that put her in the hospital for weeks.

Investigate. If you want somebody to install a brick patio, read a book or article in advance so you know at least enough to ask the right questions about construction methods and quality of material. Find out how long the firm or individual has been in business. Where did he or she get training?

Finally, one caution: Hesitate before agreeing to hire relatives or close friends. If their work doesn't live up to expert quality, it's awfully unpleasant to have to fire them.