The quickest way is to edit the /etc/exports (assuming you have root access) file on the source system (the one with not enough disk space). Then on the target system, ensuring that both hosts know about each other i.e. each host has the others IP and hostname in the /etc/hosts file issue the command, again as root:
mount <directoryname>@hostwithnospace mountpoint.
e.g. mount /usr/users/me@myhost1 /mnt
Then all you need to do on the system with diskspace issue the command:
tar cvf /var/tmp/myhost1savedfiles.tar /mnt/*
You'll need to use a location (e.g. /var/tmp above) that has enough disk space though.
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