You have posed a very good question with a very complicated answer. There are two things you MUST have in order to do what you are asking:
1) Your "docking station" cannot be the Archos mini-dock, b/c the mini dock has inputs only. Your docking station must be the Archos DVR Station - Gen 5.
2) You have to have a digital cable box, FIOS, or digital satellite box.
You will be recording from your cable, satellite, or FIOS box instead of directly from your TV. Hook the red, white, and yellow cable from one of the red, white and yellow outputs of your cable/sat/FIOS box to the specialized adapter of the DVR Station (make sure your Archos 605 is properly docked inside). Here is a link to the connection guide if you don't have it:
Once the connection is set up, you must follow the exact directions printed on pp.11-15 of the DVR Station user manual - it will require downloading several pieces of software. My only reccomendation is that you make sure that the Archos 605 is fully charged before proceeding, b/c if it loses power during the process, you may ruin your mp3 player. Here is a link to the DVR Station user manual:
If you have followed the instructions exactly, you will be able to schedule your recordings to your Archos 605.
There are two catches that I noticed with this player - 1 major and one not-so major:
1) Not-so major: Your subscription to the TV guide that enables you to schedule recordings will only be free for 1 year
2) Major: The DVR Station forces you to choose between an NTSC and a PAL format when choosing a TV standard for playback. PAL is only for Europe, so never select it under any circumstances. NTSC is shutting down on February 17, 2009 - in a little more than a month. After that time, you may not be able to display the recordings that you have made to your TV itself.
-Tha Mp3 Doctor