On the command line (Terminal), copy is done by typing:
cp source destination
To copy everything, with correct permissions and such, you'll need to add a few flags to clarify exactly what you want done.
In a terminal, if you type: man cp this will bring up the manual entry for copy.
cp -p /Users/username/somefiles/ /mnt/volumes/computer2/somefiles
for example would copy those files including permission, ownership, etc.
There are other flags which ensure you copy a directory and subdirectories, force overwrites, etc.
copying just / would copy all files, you'd just need to see which flags would best suit your job.
If there is an easier, less command-line way to do this, someone else please shout it out