All Free Agents on the Waiver Wire will have a grey flag next to their name (in the Status field). To add a player to your watch list, simply click the flag and it will turn blue. That means the player has been added to your watch list. To remove the player from the list, simply click the flag again so it turns grey.
To view all players on your watch list, click on the "On Watch List" link on the Player tab, located directly above the list of players.