To move files between machines which you can connect to via ssh, you can use the command scp. To copy a file from a remote machine to your local machine use:

$ scp <username>@<address of remote machine>:<path to file to be copied on remote machine> <destination path on local machine>

and to copy a file from your local machine to the remote machine use the reverse:

$ scp <path to file on local machine> <username>@<address of remote machine>:<path to destination on remote machine>

So as an example if I had an account called SWDG which I used to log into a machine accessed via ssh server.comany.com I could copy a file as follows to get it onto my local machine:

$ scp SWDG@server.company.com:/home/SWDG/data.zip home/personal_computer/myfiles/