Finding music that is similar to your own and making notes of the names involved in the production is a great place to start. Have your entire group do this and discuss what it is about the sound of the records that you all like and dislike. As a group you should develop a clear understanding of what you want your own project to sound like; you may find that the same names start popping up from record to record.
After collecting the names of the producers you like, research their contact information online. Most major label producers are represented by a producer/engineer management company.
Here are some resources to start your search.
http://www.worldsend.com/
http://www.nettwerk.com/producer
http://www.us.chrysalismusic.co.uk/core/what_we_do_producer_management.cfm
http://www.record-producers.com/
http://www.biglifemanagement.com/
If you don't find the name of the producer that you want to work with on any of these rosters, someone at the agencies will know who to contact. If you are still not having luck, contact the manager of the recording studio that is listed on the record. They will have the contact information for every client, producer and producer management company that they work with. Do not be intimidated when inquiring about a celebrity producer. These people are professionals and if you have the budget to afford their services, they will be available for hire regardless of your group's celebrity status.
If you find that you do not have the budget to afford a top name producer, but would still like to have this service, there are plenty of talented professionals in nearly every city working as professional music producers. These professionals may not have major label credits under their belt yet, but you could be their big break.
Recording studio managers are a great resource for a group trying to find the right people to assist in making a record. Call several studios in your area or the studio where you would like to record your project and discuss the sound you are looking for with the studio manager. This manager deals with musicians, record labels, engineers, mastering engineers and producers for a living. Developing a relationship with a top notch professional recording studio with a knowledgeable and helpful studio manager is the first step to recording a great record. This person will know or employ someone with the chops to produce your music. He will also know the various rates that producers in your area are charging and what their specialties are.
Contact and interview several producers to get a feel for their personality. You will be spending many fun, but sometimes stressful, creative hours with this person in the days, weeks and months to come. You do not necessarily have to like this person, but you need to choose someone you can trust with your project. A great producer will be results-driven and will deliver the record that you are paying to make.
There are many kinds of music producers from an endless background of expertise and experience. Some have a musician background while some are technical producers who can't play a note, but have listened to thousands of records and know how to make them. Research and listen to their previous work.
Ask questions no matter how silly they seem. You are hiring this person, so treat it like an interview and ask away until you feel you have the information that you need to make your decision.
Once you've chosen your producer, let go and trust them to do their job. You are paying them to deliver, so let them deliver. To maximize your chances of getting the best final product for your money and time, let them steer the ship. You have hired an experienced pro to handle the details of your record, and the big picture is now in the hands of an objective outside party. All that is left for you and your group to do is to play your music well, be creative and enjoy the experience. But most importantly, you must listen to your producer, because making a great record is their job and it's what you're paying them to do.