We all know the Biblical incident when the puny David with a sling and stone slayed the mighty Philistine Goliath. For God David was a chosen one and he empowered David to do the mighty deed. As an idiom it means doing the best with meager availability of resources.
Example: I wish I could use David’s sling and stone in all trying circumstances.
Many writers accomplish their works by adopting David’s sling and stone.