Having multiple characters is a huge benefit. Daily missions, you get two ascendant shards or energy.If you have three, that means six aascendant materials a day.
Nightfall, hit and miss. You can get up to 11 shards or five strange coins
Public events, now though they don't drop it anymore. I haven't seen any in a while.
As stretch said, build up vanguard and crucible marks to get legendary gear to breakdown for shards.
By far the best is the raid. You get 4 chests with a potential of I think two or three per each. You can count on the bosses dropping shards or energy and not the gear you want.