The primary way to collect shards is by using your Creatures to Reap. This action sacrifices their ability to fight for the turn but grants you 1 shard. Another common method is playing cards that provide shards, usually found in Action cards.

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Dawnshard v1.1.11 Patch Notes
Version 1.1.11 is live, Seekers! This update brings long-awaited quality of life improvements, Bot bug fixes, and a brand new way to connect with friends in battle.