Look for an expert with at least ten years of experience—you do not need someone using your money to learn on the job.
Meet at your adviser's office (not your home). If it's a wreck, your finances might end up looking that way, too.
If you have to ask about cost, you've chosen the wrong person. Search NAPFA.org for a fee-only adviser who isn't dependent on commissions from investments you make or products you buy.
Good advisers inquire about your entire financial picture, including your debts, if you own (or want to own) a home, and whether you have a will and trust. If they want to know only how much money you have, that's a red flag that they're primarily concerned about earning commissions.
If you don't understand or innately trust the person, don't hesitate to move on. And by all means, stay involved even if you find someone reliable; remember that what happens to your money affects your quality of life, not your adviser's.
Next: The one person you should never trust with your money