Players who are eligible for the disabled list (DL) are designated with an asterisk and a "DL", followed by a number indicating expected duration (in days) of the injury in red. To move a player on your team to a DL slot click on the "Manage DL" link at the top of your team page. This link will only appear in leagues which use DL slot(s).
DL-eligible players can only be moved to the DL slot from your active roster or bench. Players can not be added directly to your DL slot from free agency, as you must first add the player to an open bench slot. A player in FLB is not assigned to the DL unless their MLB team assigns that player to the DL. This does not generally happen until the start of the MLB season and does not include pitchers who are shut down near the end of the season, unless the pitcher is officially added to the DL.
To move a player from your DL back to your active roster or bench, click on the "Manage DL" link at the top of the Team page and activate the player.
NOTE: Once a player is off the DL (no longer DL eligible), the player must be placed back on the team roster before the team owner can complete another player related transaction (add/drop).