Delphi 6 Enterprise already has the Indy package installed. However, I highly recommend you download the latest update of the Indy Direct package from that website. They have full instructions on how to install it. I'm pretty sure you have to remove the existing version first, by running the Delphi setup and unticking the Indy package option.
The package comes with a pile of demo applications, which includes a mail program. The latest version on the website splits up their components on to 5 separate component toolbars.
But - basically, on the Indy Clients component toolbar, whack either an idIMAP4, or idPOP3 component onto your form. Their help system gets integrated into the main Delphi help file, so just click the component and hit F1 to get the full details on properties and methods.
So - use an IMAP component if you want to manipulate a message on the server, and use a POP3 component if you want to download the message from the server and do what you like. For example, if you want to grab an attachment from a message, and then remove it from the e-mail, but leave the e-mail on the server, use the IMAP. But if you want the attachment, and then discard the message, just use the POP3 component.
I highly recommend you have a play, and scour the help files on your component of choice, and then come back here if you can't figure it out.
But as a guide, you should programmatically set up the component to access the mail server, grab the message after checking the subject line (which I don't think you can do with a POP3 component without downloading the entire message), retrieving the messages (each will become a TidMessage object), then asking the TidMessage to save any attachments.
Good luck!
Daryl