To update a Facebook Page, as opposed to your personal profile, from TweetDeck, just add your Facebook account as normal.

Once added, on the Settings > Accounts page, you can select which of the Pages that you administer you would like to see a button for in TweetDeck.

To add any Pages that you administer but are NOT shown in the list, click Add Pages to authorise TweetDeck to use them.

Any Pages that you select on the Settings screen will then be available as buttons above the update window.

If you enable a Facebook page button and send an update, that update will be added to the Wall on the relevant Page.