Heavenly Shards are a necessary material for several enchanting formulas, and can also be used to purchase high level enchanting formulas. Patch 4.1 introduced pets that can be crafted with enchanting, further increasing the demand for heavenly shards. With shard prices as high as 75-100g on some servers, here's a few handy ways to get your hands on some shards on the cheap (assuming you have the necessary skill to disenchant heavenly shards).
Normal Mode Dungeons
While heroic mode dungeons are perfectly fine for obtaining shards, normal mode level 85 dungeons – Grim Batol, Halls of Origination, and Lost City of the Tol'vir – are a relatively safe and efficient way to obtain some shards. Especially if you are a well-geared tank, these runs will be quick, painless, and profitable.
Three Small Ones
Keep an eye out for cheap Small Heavenly Shards on the auction house. For instance, if heavenly shards typically go for 90g, picking up a small shard for 20g would be a wise investment. (Keeping an eye out for cheap Heavenly Shards is also wise!)
Disenchant Your Blues Away
Some crafted blue items – such as leatherworking cloaks – will often AH for less than the price of a heavenly shard. Any blue item that requires level 83 and up will always disenchant into a heavenly shard! Check the AH regularly and you can pick up several half price shards using this trick.
Quests Are Always Win
Complete all of the quest lines in all of the Cataclysm areas – especially Uldum and Twilight Highlands. Make sure to do all of the dungeon quests as well. All of the armor and weapons provided from quests that you don't need (that is, most of them) will provide a treasure trove of enchanting materials, including heavenly shards from the blue items given at the end of the long quest lines.
For Great Justice Points
If you've got a heap of justice points burning a hole in your backpack, trade them in at the Justice Point Trade Goods vendor for heavenly shards! While they're rather expensive to obtain this way, it's a smart move if you have no other use for your justice points.