They should give you access to FTP, in which you should download and install FileZilla(Free FTP). If no ftp access then they definitely should have a file manager in the control panel (something like photobucket if you ever used that).
Completely ''free-web-hosting'' is a myth and therefore you will not be able to obtain a .com, .org etc. for free. However, when companies mention that there is free web hosting, they are referring...
Good free web hosting sites can be found many places. One of the best is one called Blogspot. Here you can find free web hosting and have the option to upgrade.