First of all, you have to be familiar with linear audio editing software, for example Adobe Audition. You have to be experienced with this piece of software, as audiobook editing means loads of content that needs to be listened to and edited to perfection. So if you're familiar with sound design but you cannot edit audio fast enough you will struggle with making deadlines. Not to mention that payment is usually per hour of edited content, so if that takes you 5 hours then your rates go down by a lot.
You can always start editing podcasts first and then graduate to audiobooks. Speaking of which, the right people to contact would be voice actors, narrators and content creators at first. Once you complete a few (e.g many) small projects you can think about contacting large companies or publishers.
As I already said, the fees are usually per hour of edited audio. If the raw audio is extremely bad you can negotiate per source audio rates.
One skill that's definitely required is patience. Audiobook editing isn't as glamorous as sound design for media, or as thrilling as writing music for video games. You just listen to hours of content on end and edit out imperfections until your ears bleed.
Obviously, clients will be looking for before and after excerpts from projects that you've worked on.
For more info and maybe opportunities you can check this out: http://www.acx.com/