To make an FTP connection you can use a standard Web Browser (Internet Explorer, Mozilla Firefox, etc.) or an FTP Client. To establish an FTP connection you need to have an FTP hosting account where you plan to upload your files. You can also create additional FTP accounts for other users.
When using a Web browser for an FTP connection, FTP uploads are sometimes very slow, and downloads are not protected (not recommended for uploading or downloading large files).
An FTP Client is a software designed to transfer files back-and-forth between two computers over the Internet. It needs to be installed on your computer and can only be used with a live connection to the Internet.
With an FTP Client (such as FileZilla or CuteFTP) uploading/downloading a file is really easy. Furthermore, FTP clients have some extra features. For example, you're can resume a download that did not finish successfully. This is a very nice feature for people with slower Internet connections.
FTP clients' interface is usually divided in two - the pane on the left shows the files and folders on your computer (your Desktop, My Documents, etc,) and the pane on the right displays the files on the remote Server (if this is your website hosting account, you will see the public_html folder, where the files of your site are stored).
File transfers are made by simply dragging and dropping files from one pane to the other. Additional features of the FTP Client include: multiple file transfers at a time, auto resuming of the transfer, file queueing and more.
You can read the following tutorials for two of the most popular FTP clients: