Not a programmer myself either, especially with Java, but from what I've played with the issue I'd say it would be easiest to start with Funambol Exchange connector. It uses WebDAV to talk to Exchange, and
AFAIK Zimbra provides same interfaces. It might be as easy as just modify configuration UI to configure correct paths (it looks like the http uris are hard-coded in Exchange connector).
There was a mention of Exchange connector supporting also Zimbra in some version of Ex-connector documentation, but it did not specify how to configure it. At least I couldn't make it work.
If you/someone starts to look at it, I'd be happy to help with testing etc.