Copied this from VG24/7 website.
Destiny: The Taken King makes big changes to the Legendary Marks system. Find out where to acquire this vital currency.
There are only a couple of known sources of Legendary Marks at the moment, and we suspect Bungie may fix that soon. This is the most sought-after currency in The Taken King right now, as you need them to buy gear from the vendors and ascend armour and weapons to raise your Light level. It’s only by doing this that you can hit the Heroic challenges for the best drops and, obviously, get prepared for the new Raid when it unlocks on Friday.
Arekkz has all the details on where to get Legendary Marks at the moment (see below), but here’s a breakdown of the info in case you can’t watch the video. No video, again, copied from VG24/7 website
You need to be level 40 to start earning Legendary Marks.
You get 15 Legendary Marks for completing the Daily Heroic Story mission (level 41, recommended 240 Light level). Remember, this is now account-wide, so you can’t farm 45 Legendary Marks with your three characters. You do it once, and that’s it until the following day.
You get 15 Legendary Marks for hitting the Daily Crucible Match. Again, this is account-wide.
You get 10 Legendary Marks from the Weekly Heroic Strike. All three of your characters can benefit from this.
Some story missions reward you with Legendary Marks. Check in your Quest tracker to see which ones.
Dismantling year-two purple armour and weapons gives you Legendary Marks. You get three from an unlevelled item and 4-5 from a levelled item.