There are a number of options, which one is best depends very much on where you wish to make most of the changes, how big the files are and whether you want to support more complex things like differential copies.
The simplest way to do it is to set up a network share on one of the servers and pull or push data to that share. Ubuntu can provide remote shares using either NFS or SAMBA, the Windows box native file sharing can work with the Ubuntu SAMBA stack and you can add NFS services to W2K8 if you want. In my experience it's simpler to set up the W2K8 box to access an NFS share rather than set up an Ubuntu system to access a Windows share via SAMBA but the difference isn't all that significant and if you are more familiar with Linux or don't want to install anything additional at all on the Windows box then go the SAMBA route.
If you prefer to use NFS then you will need to add\enable File Services for NFS on your Windows 2008 server. Once that is installed you can set up either side to handle the NFS exports and connect the other system to it. There is a straightforward guide to enabling VFS Client\Server components on Ubuntu here on UbuntuGeek. Once you have a share mapped between the systems just use whatever scripting\scheduling tool you prefer to push or pull the file(s) across as needed.
Other options like rsync, scp, sftp can be used to transfer files too but all require some additional third party server or client components on the Windows box which may not be ideal but they can offer advantages over the NFS\SAMBA option.