When using the Computer Science Linux machines the files are stored on a server that is accessible from all the CS managed linux machines without you having to do anything. If you do all your work and submitting from these Linux machines you should have no problem accessing these files.
If you are doing work remotely and/or need to transfer files between the Linux machines and your home machine you will need to transfer the files using what is called Secure File Transfer Protocol (sftp). This allows you to copy files from your Linux filespace on campus, to a remote machine. There are utilities provided by the University of Iowa that can make this an easier process here (ITS Software Download Site).
For Windows users I would suggest the WS_FTP program. A tutorial can be found here (WS_FTP Tutorial).
For Mac users I would recommend the Fetch program. The process of using Fetch is similar to that of using WS_FTP.
To connect to the Linux machines you must specify the server and login/passord information to gain access to your files. The server you should connect to islinux.cs.uiowa.edu.