Hearthpwn

The game plan here revolves about trading efficiently with the White Knight: the ability to pick your target and the fact that it has 4 attack must be used to its fullest along with the White Bishop.

Always mulligan for 2-3 White Pawns and hope that you'll draw into the Knight and Bishop. Once that happens, it's a matter of positioning.

Make sure that you always place or switch the Knight to the rightmost slot, and the White Rook (more often that not) on the middle, to tank damage, use the Pawns to modify the number of minions to an odd/even one or to an even/odd one, since you'll have the upper hand at the end of the turn.

Regarding the Bishop, placing it between Pawns is a good strategy, because it simply tanks damage while it heals your other minions. Use the hero power to switch its place from either the Knight's vicinity or the Pawn's to the injured minions, or, if need be, move it to the left-most place to sacrifice it for the attack power; in the end you need to attack, not to defend, since your resources are limited, his aren't. The ideal use of this minion is to trade and heal the Knight. Healing the Queen is a good option as well, but since it has 6 health, healing the Knight after hitting a Rook/Pawn is more important imo.

In the end, the Queen isn't used as a finisher, but as a board clear, having a Bishop between the Queen and the Knight being the target that you should go for.

Pictures:

 I hope this could be of help, even if just a bit!

EDIT: Thanks for the feedback, I appreciate it! The turn one pass tactic works as well, however, think of the real chess game: Pawns are pieces that are sacrificed, in the end, even if you lose your Queen, as long as the King is alive, you can still win. Having a board is detrimetal, so I prefer to have board advantage over small damage ticks to my face, since you'll never know if he'll play a Knight/Bishop, the Bishop is the most favorable case since you can play your Knight to counter his Pawns and then go for double hits if possible. That's just my opinion though, both options work, though I prefer the one that implies board control