Repeatedly select the "Try Another" option until you matched with someone who is about the same level or lower than you. After winning a match, you will get two stars until you lose. Because you can never lose a rank, attempting this against slightly tougher opponents is fine. Ignore their PvP Rank, as it does not indicated anything important. However, losses will cost gold. Note: You can pay for souls and level your minions without actually leveling your hero. Additionally, manual defense fights that are won will also count as PvP victories and also advance your rank.
You must gain enough souls to upgrade your units. Use your gold to do this by spending gold to get keys, then units, then souls. To transform units into souls, select "units" then "disenchant".
If you have a chance to match four or more mana orbs, do so. Even if that match does not directly benefit any of your fighters, you will receive an extra turn that may become useful after the pieces have shifted. Additionally, making the match blocks your opponent from making it.
The order of your fighters is important. The first fighter in your line-up will execute physical attacks when three skulls become lined up. Also, mana goes to the first fighter in the line-up that has the corresponding rune.