If you have two players, one with Destiny and the other with Destiny: The Taken King, how does multiplayer work? That is, if you're playing Destiny: TTKM are you matched with older Destiny version players or no?
Destiny DLC is not part of the main game and are specific missions, PvP, raids, etc. If you're using the DLC content in multiplayer mode for say, a mission - the only players you'll see in the DLC content are players with that DLC.
Players without the DLC can see DLC specific places and player loadouts, banners, etc., but they cannot obtain them without the DLC either.
However, I'm not sure what you mean by "two players" but if you mean two characters on the same system then the DLC should apply to both. If you mean that you have two people you play with, the one without the expansion won't be able to participate in any of the expansion content.
When you are in a party and attempt to to an expansion mission or raid, you'll be told someone in your party can't participate - they will need to drop from the party or you'll all have to cater to lowest common denominator.