The two easiest ways to get shards is by doing HBM (Here Be Monsters) and Dungeons. For HBM, A gives you 10 shards per completion, B-15, C-20 and so on until J which gives you 55 per completed 5-round run.You get one HBM run every 3 hours and can store up to 6 tries.
For Dungeons, try to raid those with a flame - they tend to give more shards than the normal ones. Keep in mind that, while a completed HBM will always give you shards, completed dungeons don't always drop shards. In my personal experience, on average 1 out of every 4 tries gives shards.
The third source of shards is by doing your daily quests. Some of the tasks' rewards are shards.
There are other ways of getting shards but these are the 3 main sources.