Some good methods:
1. Go to a bookstore. Find books like yours. Write down who published them.
2. Get a copy of Writer's Market.
3. Look on
Preditors and Editors.
4. See who's buying books on places like Publisher's Lunch.
None of these methods are foolproof. A local PublishAmerica author may have convinced your local bookstore to sell his book, scammers have been known to slip into directories, and Publisher's Lunch certainly does not cover all reputable publishers. So once you've found a possible publisher, check things like online bookstore databases to see if their books are stocked in stores, and check it out in the Bewares and Background Check forum here.
And once they start negotiations, there is one obvious sign you've found a good publisher:
They offer you several thousand dollars as an advance and a contract that doesn't suck.