You can use 10 legendary marks to purchase 20 of any planetary material from the Vanguard Quartermaster. See below to locate the quartermaster.
Faction rep (per each of the 3 factions: Dead Orbit, Future War Cult, New Monarchy) can be gained by speaking to the respective faction rep in the tower, as seen on the below map. The exchange rates are as follows, gaining rep for the faction rep you exchange with:
5 Motes -> 100 rep
25 Weapon Parts -> 50 rep
25 Old Armor Materials^Materials✝ -> 50 rep
25 Unified Armor Materials -> 50 rep
Special Ammo Synth -> 25 rep
Heavy Ammo Synth -> 25 rep
✝ ^OldOld Armor Materials includes Plasteel Plating, Sapphire Wire, and Hadronic Essence.
EDIT: The below exchanges are no longer valid as of "The Taken King", September 2015.
You can now go to the Vanguard/Crucible Quartermaster and exchange 10 marks for:
20 Spinmetal
20 Helium Filaments
20 Spirit Bloom
20 Relic Iron
The Crucible Quartermaster is in the middle area of the tower before the class Vanguards (opposite Lord Shaxx). On the map this is in the blue area near the icon that says Crucible.
The Vanguard Quartermaster is in the area near the shipwright. On the map this is in the red area and marked Quartermaster.
EDIT: The below is no longer true as a of a patch in late 2014.
Each time you exchange 50 of each material to either the Crucible or Vanguard Quartermaster, you get:
+5 Crucible/Vanguard Marks (as long as you're below the weekly limit)
+25 Crucible/Vanguard Reputation (these change if you have a faction class armor equipped)
+250 Glimmer
Note that you are also capped at 200 total marks for each faction, and 100 per week for each faction.