There are several ways to transfer files with SSH.
scp (secure cp) - basic syntax is scp -r what where. what and where are either local files or remote ones. In the latter case, it is in the form [[user@]host:]file - e.g. arthur@camelot:path/to/file denotes a file located on computer camelot into which scp is supposed to log as user arthur; if the pathname is relative, it is relative to remote user's $HOME.
sftp is an interactive FTP-like shell.
tar c files | ssh user@host tar x - pipe a tar archive through ssh connection to tar spawned on the remote host. Can be reversed (ssh user@host tar c files | tar x). If you need to transfer just one file, using cat is also an option (TAR will keep file permissions and modes though).
SSHFS - FUSE-based user mountable file system backed by SSH, which offers seamless integration into the file system hierarchy.
In all cases you have to have the SSH daemon running on at least one of the two machines. To find out hostname use the hostname utility. You can also use the IP address instead of the hostname - to find that one out use e.g. ifconfig or ip addr (on Linux, I don't know what is used on Mac OSX, which is of BSD heritage). If you have OpenSSH (which is very likely) check the man pages - they are rather well written.
An alternative (at least on local network) can be e.g. full encrypted NFS (v4+) export, which however is more difficult to set up (might be faster though, unless you use a specially patched version of OpenSSH targeted at HPC).
scpandsftp. – derobert Mar 20 at 22:58