The deck is designed to maximize value. Get your damage in on your turn before your opponent can respond to it and, if they don't, get more damage in. Turn your creatures into 2 for 1s by pinging them to death. Calvary is a must, using Charge to deal three damage then be a creature that needs to be addressed. Maximizing minion threats that do side damage.
Use minion pings to clear as much of the board as possible from enemy threats and bury, disintegrate, infiltrate, and earthquake the rest.
Flame Wave is your big finisher (or a way to clear the board if you get in trouble). Don't throw all your direct damage in the bin though - save that Flame Wave if at all possible to end the game. Last thing you want is for them to pillow-fort while at Death's Door with no way to finish them off.
Try to get a starting hand with a Stone, Core, or Settlers in it. Most of the deck is VERY cheap to cast, so it will be rare to dump a hand and end up with really high cost spells in hand. If in doubt, mulligan hard.
Save the Pillar for later in the game if at all possible. Smokestacks can turn off troublesome land you are facing. Put Vesuvius in the middle of the board and zap their creatures if they get too greedy. River of Flame will let you Infiltrate and Disintegrate Spiders. Your deck needs 2 earth and 2 fire threshold, so make sure your opening hand is solid. You don't want to be digging for sites when you could be drawing spells. Get 4-5 sites in play and start double-drawing each turn.
Once you have 4-5 sites and have the board stabilized you are drawing 2 cards per turn and trying to turn your creatures into 2 for 1s, which should give you a good chance to overwhelm the opponent.