Your best bet would be to look in the docs folder of your Zimbra installation (usually /opt/www/docs if you are on linux) and have a look at soap.txt, soap-admin.txt and rest.txt depending on what you want to achieve.
The rest APIs are generally great for downloading a user's mailbox and other content such as contact and calendar entries as an archive, in case you want to back them up.
The admin apis are useful for managing the server and its users, checking the status, flushing the mail queue, etc.
If you want to implement client(user) functions, have a look at the source code for the Zimbra desktop client.
There is a post here which provides a (partial) Java compliant WSDL file for the Admin SOAP api, and also a jar containing ready-to-use client proxies generated from them with CXF.