The software that is used to move files from one computer to another connected computer using the internet is called an FTP Client. It has to be installed in the computer and you can only use it when connected live to the internet. A traditional look of an FTP Client is a two-paned design. The files on your computer can be seen on the left pane while the files on the remote computer can be seen on the right pane.
Transferring of files is done easily by just dragging-and-dropping the files from the left pane to the right or vise versa. Files can also be transferred by highlighting a file and then click a direction arrow which is located between the panes.