Fastest way to grind each resource?

[Arcanix]

What the fastest to grind the resource for new player? the glimmer, legendary shards and bright dust

[Illusive Soul]

Dares of Eternity.

[`digitaL.braVo]

Get stuff and dismantle it. Just make sure you save good rolls or rolls that MAY be good later.

[JARK]

BRIGHT DUST
Do as many seasonal challenges as possible; as you "level up" in the game you should be able to tackle harder ones. Many are available even if you're a F2P player.

For smaller but more permanent sources of dust, do repeatable playlist bounties (the bounties that 3000 glimmer, from Zavala, Shaxx and Drifter) in addition to other bounties from the playlist factions. Doing 8 bounties per week per faction yields a small amount of dust, per faction, per character.

GLIMMER
Just play the game. If you're short, slap on the +glimmer ghost mods (see 2nd or 3rd slot on your Ghost item section). You will eventually wonder what to spend the glimmer on, rather than wondering if you have enough, lol.

Public events and world activities are great sources of glimmer, as is just running around world maps and opening chests or picking up environmental resources (these usually have a "glow" to them; you can see where they are by equipping ghost mods in the 2nd column slot).

LEGENDARY SHARDS
When farming playlists (Vanguard, Crucible, Gambit) equip the relevant "Prosperity" mods on your ghost's 4th slot. You'll get a chance for 1 extra legendary loot. Otherwise, just chase powerful and pinnacle gear drops, which pretty much come from doing anything enough times. Open loot chests from repeatable world activities like Blind Well, Altars of Sorrow. Dares of Eternity is a good farm as well, and fun.

Dismantle all loot that is crap but ISN'T at the highest current light level (e.g. if your level is 1780 and you got a new weapon that dropped at 1781, keep it). Always keep the highest-level loot until you get a piece of the same inventory section slot that is higher (e.g. kinetic weapons, energy weapons, power weapons, head armour, etc.). The game reads your entire inventory + vault to see what your highest class-specific gear is (i.e. any weapons + class-specific armour) when computing your maximum POSSIBLE light level average (your current light level from equipped gear may not be the max possible; it is the max possible that matters when acquiring new pinnacle gear, which drop above your max average).

At times you may also want to use more powerful gear to infuse good gear that are at lower levels. This is another reason to keep the most powerful gear around, even if they are crap stats/perks. Just keep in mind that if you're infusing one gear in every slot section per week (5x minimum per week per character), that adds up to a LOT of upgrade modules (an UM is not necessary if you're infusing duplicates), and every time you infuse you lose out on the shards you could've obtained from dismantling. I'd save most infusions for the pinnacle grind, once you reach the powerful cap of the season (currently 1800).