In 1v1 mostly, PvP is basically who can have the best advantage in the situation. There are several aspects that can come into play in a 1v1 match that can offset the balance of who has the advantage. One of the most noticeable one is the turn advantage, or who goes first. Although, you can still win from going second but more pressure is applied to you while going second. There are spells that can change the advantage, but many players know to get rid of it and/or put up their own advantage. These are called "Wars," where players try to remove the others advantage and set up their own.
The pip war is basically the pip advantage you have over the opponent. If you have 5 power pips and your opponent has 2, you have the advantage because you have a better chance of successfully pulling off a combo that could ultimately end the game. Many things could delay such combos, such as shields, weakness etc. The pip war is the MAIN advantage which people try to disable by playing various tools that could help your opponent waste pips. Always try to have the pip advantage over your opponent, unless you can set off the combo to win the game. You could offset the pip difference by forcing your opponent to heal.
I don't think I have to explain this one much because it's very obvious. Technically, Ice is almost always winning the health war. Health war is also how much you can heal off the damage your opponent deals. The crafted ring and athame from Celestia give you the advantage of this. Infection is a great tool to get you the advantage in the health war, so is Life dispel. A more in depth talk on infection could be found here.
This war is one of the most important to win. Some schools can not win the bubble war most of the time because it is not pip efficient, for example Death, Life and Balance. The rest of the schools have 2 pip damage boosting bubbles. If you are Ice, Storm, Fire, or Myth, and you are facing a Death, Life or Balance you can go ahead and put up your bubble because more likely than not your opponent can not win the bubble war. If you are facing a school that has a 2 pip damage bubble do not put up your bubble unless you want them to waste a turn and put up their bubble again in this case you can go ahead after they waste a turn putting up a bubble you can shield or dispel them if you are going second. You never want to put your bubble up if you are facing the same school you are playing that is just your death sentence. A bubble is like a blade but it stays up forever, usually most people don't carry much blades just a bubble. From what I've seen Fire, Ice and Myth are great with their bubble up because of their DoT spells and Double hitters. Bubble wars are found most commonly in 1v1 matches but can be applied to group matches if played well. You definitely don't want to beef your opponent up.
This tends to be over looked in early rank matches. Some players think that a minion is no big deal, and should just attack their opponent. Let me tell you, a minion out could be, but not always, the winning factor in a match. Since KI updated the minions, they have become a reliable ally in most matches. A minion can make you lose the pip war as both the opponent and his minion gain pips faster than you can. An opponent with a minion can deal more damage the just one wizard alone. For schools with 4 pip AoE spells, minions tend to be less of a problem with a Gargantuan Blizzard or Meteor, you have done damage to the opponent and got rid of their minion. The best minion in MY opinion is the Fire Elemental, it can cast smoke mantle and get rid of shields and puts up fire traps and shield you with a Glacial shield and it also heals you. Cast your minion when you know your opponent can't kill it the next turn either by low pips or something of the sort.
Very few battles end up being on who has the better pet. The only time this could happen is if when both sides are completely equal and cannot take each other down. This is when the pets come into play. Let's say a player with a Star fish has the talents Spritely, Spellproof, may cast Ice blade, and Health gift, now lets say the other player has a Fire serpent with Spritely, Spellproof, Defy and Paingiver. The Fire Serpent has a fire card which the caster can use, and is reliable unlike the star fish with Spritely and Ice blade. These may cast talents are all based on luck, which eventually determines the outcome of the match. The generic talents which increase the casters stats are reliable however and can determine the match as well. This is why the fire with the Fire serpent has a higher chance of winning the match if both casters are at a stand off and can not take each other down, this is why strategy is important so you do not have to rely on your pet to win the match for you.