Can you please provide a little more information? My immediate questions would be:
Have you already mounted the network drive on your Mac through the finder?
If not ...
Are you trying to connect to another Apple operating system (in which case you probably will want to use Apple Filing Protocol (AFP) (your URLs when connecting via the finder would probably look something like afp://server/share))
Are you trying to connect to a Microsoft system (in which case you probably want to use the Server Message Blocks/ Common Internet File System (SMB/CIFS) protocol (and your URLs will look something like smb://server/share))
Are you trying to connect to a Unix / Linux like system (in which case you probably want to use Network Filing System (NFS) (and your URLs will look something like nfs://server/share))
Are you trying to connect using Web Distributed Authoring and Versioning (WebDAV) (in which case your URLs are going to look something like http://server/share)
These are just the common networking protocols. There are others.
The very first option (connecting to the share using the finder, then using standard Java) is the easiest option for you as a developer. (There is always a tradeoff between amount of work performed and user experience )
The list of protocols / operating systems should only be considered a guideline (at best). They are the protocols that the relevant operating systems would normally use by default if they do not have to worry about interconnectivity. But there is no reason why a system running one of the Microsoft OSes could not be supporting NFS. Likewise a Linux system could be supporting SMB/CIFS and/or AFP.
Once you have answers to some of these questions, you could try plugging the name of the network protocol and the word Java into Google and see what sort of libraries you come up with.