After you make it to level 20 in Destiny you will need ascendant materials to level up farther and upgrade your weapons and armor. A single piece of Exotic Armor can require up to 32 Ascendant shards and the same goes for Ascendant energy weapons. These are some of the best ways I have found to get the materials you need.
Just kidding, this is one of the worst and most time wasting activities you can do in Destiny.
Dismantling Armor and Weapons (Any Level) – Always Available
Buy Exotic gear from Xur and Dismantle it. I would suggest against this method, but if you really need to you can dismantle legendary or exotic weapons and armor for ascendant materials. Personally I like to keep all my weapons and armor for as long as possible until I start running out of room in my ATM… errr Vault. I’ve dismantled some things that I wish I had kept later on, but at the time I was greedy and needed to have materials right away. I find that the Exotic chest pieces drop the most when dismantling and they cost the same from Xur as all the other exotic armor. Find where Xur is at the tower using http://www.hangingwithxur.com.
Public Events (Any Level) – Resets Daily.
They happen at random times, usually every 15-30 minutes, while you are doing a Patrol Mission on any of the planets. The first public event you complete on gold level any given day almost always awards you at least one ascendant material. I’ve had instances of doing four public events in one day and getting one to two ascendant materials every time… I’m not sure why it happened or how to recreate it, but I always try to do one a day. It takes only a few minutes to complete the event and if you use a tool like http://www.destinypublicevents.com, you will have no trouble finding an event.
Daily Heroic Mission (Level 28) – Resets Daily.
A daily heroic mission is a different story mission chosen at the beginning of each day with the heroic modifier active. The daily heroic missions are guaranteed to hand out two ascendant materials if you do it on hard level 28. Most of the time I can solo these but if you are a lower level, say 26, you may need some people in your fire team to help.
Weekly Heroic Strike (Level 28) – Resets Weekly.
The weekly heroic strike is a watered down version, same as nightfall but fewer modifiers active, of the weekly nightfall and you can only complete it once a week until reset every Tuesday morning. You don’t always get ascendant materials for completing the weekly heroic but you do get nine strange coins if you beat it on hard level 28. You can then turn in the coins to Xur at the tower on the weekends and grab yourself some exotic gear which can be broken down for their ascendant materials.
Weekly Nightfall Strike (Level 28) – Resets Weekly.
I usually get two ascendant materials and a legendary weapon for completing the weekly nightfall. Sometimes instead of a legendary weapon you can be rewarded, in my experience, up to 12 ascendant materials.
Vault of Glass Raid (Level 26)
Each time you beat a boss in the Vault of Glass you “can” be rewarded with ascendant materials, legendary armor or weapons, and exotic armor or weapons. I say “can” because the last time I beat the final boss Atheon , I was rewarded with two ascendant shards and a shader. You can imagine the words that came out of my mouth when that happened. I have yet to beat it on hard, but I would think it just gives you more, like every other mission and strike at a higher level would. Also there are various chests hidden in between boss fights in the vault that generally give out at least two ascendant materials.
Lastly but the most effective method.
Create Multiple Characters
In Destiny you are allowed to create up to three different characters. I have two Warlocks and one Titan. My Titan is a level 28 and one of my Warlocks is a 29 and the other is a 26. Utilizing the ATM vault at the Tower I can exchange gear between all three characters and share the armor between my two Warlocks, essentially giving me two 29 Warlocks. You can multiply your earnings three fold using the above methods and then store and share everything to your other characters using the ATM.
Hope these tips helped you out!