The most popular protocol is FTP (File Transfer Protocol). There are many client programs available that implement the FTP protocol. Most web browsers have ftp access (for download only) available by providing a suitable web address. For example, you want to transfer files in your home directory on the server onyx.boisestate.edu to your home computer and lets say your login id is jhack. Then specifying the web address ftp://firstname.lastname@example.org will pop up a window for password, and then give you access to your home directory on onyx for downloading. However, this technique does not work for up-loading files from your home computer to a departmental server. For that you will have to use a ftp client program. Under Linux, a good graphical client program is gftp. Graphical ftp clients are also available under MS Windows and MacOS.
Many systems do not allow FTP access to user's accounts since normal FTP programs send your password on the Internet unprotected. The Secure FTP protocol sends passwords and data encrypted. Most browsers support Secure FTP protocol. To use you would use a web address of the form sftp://email@example.com.