The main idea behind this deck is using Anka, the Buried to reduce either Aya Blackpaw or Carnivorous Cube, or both!  You can then use them to generate a lot of tempo on board in a single turn, especially if you have a single charge that you can use on Necrium Blade after cubing Aya, or if you reduce them both to (1) 1/1 you can use Necrium Vial on the Cube as well.

Generally you want to try and play this deck for board control early on.  One way to do that is if you can play Jade Swarmer and Unearthed Raptor to copy their deathrattle.  That way if the enemy clears the board you at least still have some jades remaining.  An early Necrium Blade also helps, but can be tricky if you don't have the deathrattle minions on board when you take that second swing.

Card generation from early minions can help ensure you don't run out of resources, and Sonya Shadowdancer can be played at strategic times to generate more minions.  Jade Spirit and Swarmer are especially good targets to generate through Sonya.  One of my favorite uses for Sonya is after Anka hits Aya and Cube, play Aya and Sonya, Cube your Aya for an additional Aya in hand.

I previously had Spiritsinger Umbra in this deck, but often she felt clumsy and stuck in my hand for a long time, or I'd draw her too late and she'd become useless.  I also originally had a Cavern Shinyfinder to draw a weapon, and an extra weapon in Shadowblade for extra control and/or face damage.  I removed them in favor of the Vial, Spellbreaker, and a second Elven Minstrel as I often would rather combo for two minions than pull one weapon.  But that's the extent of the optimization of done to the original list.

The deck is sitting pretty much at 50% win rate at mid-ranks of Wild ladder, so I wouldn't suggest spending the dust on crafting expensive pieces if you don't have them.  However, if you have the pieces I would give it a shot!  It can win fast with the right draw, but often performs better against slower opponents.