the best way to farm exotics in destiny is talking to xur and playing nightfall all day but play at least on hero or legend difficulty to get exotics faster because it is very common to get them on those difficulties and more higher difficulties.
The best way to get exotics is to maximize doing activities which have a higher chance to drop them. Do these things for maximum chance:
- Do all Powerful Rewards on all characters. Every single Powerful reward has a chance to be an exotic instead of the normal reward. So do all your Crucible/Strikes/Gambit/Heroic Story/Heroic Adventure/Flashpoint/etc... - each day that one of these resets, do it again - Do all Dreaming City activities every week (Ascendant Challenge, Blind Well/Offering to Queen bounties, featured story mission, bounty for 8 daily bounties). - On Curse Week, do Shattered Throne on all characters - If you Raid, do the Raid every week on all characters
Once you exhaust all your powerful rewards (I'm sure there are some I forgot to mention), then you are going to be limited to hoping one drops in the Wild as an engram. Focus on activities that have a lot of enemies - the more enemies you kill, the more chance you might see one drop.
Just doing all my powerful rewards this week, I got Trinity Ghoul, Ursa Furiosa, Shards of Galnor, Geomag Stabilizers and Queenbreaker (my luck this week is not typical but if I had not farmed all my powerful rewards, I would have never gotten them)
The easiest way (but probably the most time consuming) is to buy a bunch of vanguard boons from Zavala and use one at the beginning of a strike. Need 2 people in your fireteam. Quit out and repeat until you get your exotic reward pop up.
