Purchase a copy of Writers Market or subscribe to Writers Market online. There are plenty of publishers, including major publishing houses such as Harper Collins and Random House that consider audio books without requiring print versions. These publishers and others are listed in Writers Market.
Browse through the market listings and make a note of the markets available. The Writers Market listings give you complete submission information, contact information, tell you what the publisher publishes and what you will be paid. Look for those publishers who do audio books specifically.
Package your manuscript according to submission guidelines. Don't send an actual recording of your audio book unless specifically requested by a publisher--and this is rare. A poorly recorded book could ruin your chance of publication. Also, book publishers prefer to handle the recording of the material, and many major book publishers have their own facilities.
Wait the appropriate amount of time before sending a follow-up on your submission. Guidelines will typically be listed in the market guide. If you have not heard anything by then, follow up with a letter inquiring about the status of your submission.