I have done a lot of dueling in the Arena, and I am sure I have more ahead of me. Why don't you check out my tips? They can turn the tide for you in any battle, and I would enjoy that you read them in the first place anyhow.
The most important thing to remember is what you do BEFORE you begin dueling. You will have a great advantage on your side if you do Practice PVP. Note that you can check out the kind of people you will be allied or facing off with. Remember the Triangle of Magic? You can see a person's school of magic, and also the most likely element that they will use. Ally with a team that will have effective magic against the other team, using the logic of the Triangle of Magic. Same vice versa. Look closely at your deck's wards, and try to challenge a team in which you can shield yourself against. Look for spells like Weakness or Tower Shield as well, that way you can be prepared for any kind of magic. If you will have any other kind of magic in your deck, make sure you look closely at the kind of spells and the fizzle and attack rates.
You can also look at other player's levels! Point to the magic icon for each player to see their level. Needless to say, pick the team with higher-leveled players, if you want a win.
If your creating your own battle, you can make your team or an opposing team friend exclusive. With that, you can easily control the handicaps of the battle.
However, these only work on Practice, so let's move on to battle tactics.
One advantage is which team goes first. It is at random, however, so don't rely on this too much. Now for the fight. Take my word for it, NEVER start a battle with an attack. It is a sign of weakness to the enemy. Cast a ward or blade on yourself, or put a trap or mantle on an opponent. Make sure you lots of these kinds of spells, so you can do it whenever needed. Usually, these are zero rank spells, so you can save your pips for bigger attacks. When the battle heats up, put these spells on the opponent with the MOST PIPS. A mantle will weaken their attack, or a trap could agitate them into wasting pips on healing, or turns on defense. You can ultimately erase an opponent's power doing so, and all you lose is a single turn.
The kinds of spells you use are important too. Try to focus on using spells with your school's magic. Power pips only work on your school of magic, enabling you to attack consistently, putting pressure on the opposing team. But there is now problem with using treasure cards. And, if you have one, keep a healing spell in your deck. You never know when an opponent will break out a strong move.
When attacking, try to focus on the WEAKEST enemy. The enemy will have to waste pips and valuable time to heal the other players, giving you time to plan out how you strike. Use strong attacks, and make use of your time with preperatory spells.
If you want to make sure you always have a certain spell at hand, put in many copies of it. That will increase the likelyhood of having it in your hand at the right time. Treasure cards stay in your hand until you use them somehow. But if you discard one, it is gone for the battle, so be careful.
Got a minion spell? Use it. Minions are usually weak, but you can use them to distract your enemy, so they will attack your minion, not you. That would be a good time to heal or shield yourself if you are low on health. Forget the usual calm or distract spells. It MIGHT effect fizzle rates, but it won't stop them from attacking you.
Speaking of minions, people who join 3vs3 duels probably will have a minion spell. Note that, read it twice.
In fact, a person's stradegy can differ depending on what duel they join. Of course, 4vs4 is the most popular, so join if you just don't care and want to jump right into battle.
Ranked matches can earn you tickets to buy furniture or attire. My opinion? Get new clothing. The clothing there is exclusive; you can't get it anywhere else. They can be really helpful in future Arena matches. The things you have equipped can completely change the outcome a battle.
Do something with every turn you have. Each is vaulable, so never pass one up. A shield, blade, trap, mantle, even a weak attack may all come in handy when you least expect it. I know that first-hand.
I guess I'm out of tips now. Oh well, I couldn't go on forever. But don't think I'm the expert at this. I'm not even a Grandmaster Wizard. If you have any tips, I would really appreciate you telling them to me, so please write back.
another important thing to do is to know how to use your primary school to it's highest potential, as well as any secondary schools you have. as a balance/death/ice wizard, my strategy is to use 0- or 1-rank spells like shields, blades, traps, etc to save up for massive attacks and heals in a pinch. there are awesome ways to utilize any combination of schools. a person who knows storm will want to use the strategy i do: use boosts and shields (don't forget your lightning strike!) and then utterly vivisect the enemy. know life and ice? couple the "save for the heal" strategy with the "peashooter" (in which one gradually wears the enemy down with a steady barrage of rank 2-4 attacks).
another useful thing to do in practice pvp is to battle a variety of schools combinations, to get a feel for what you can expect.
this is also helpful: tricking the opponent into letting their guard down. one thing i do is put on a badge one gets at low levels, such as "hero of unicorn way". this can make them think you are not a threat... until you blast them with a powerful spell. another way - i am ashamed to say i have fallen for this - is to (this might sound desperate or even cowardly) plead for mercy, pass, maybe put up some shields. the enemy will either be saving for a 1-hit ko or be toying with you like a cat. then, once you have enought pips, traps, etc... use a rank 4+ attack to blow them away.
as a fourth and final piece of advice, i advis you to organize your deck well. make 40-50% of your deck attacks, use a high amount of heals, and have multiple 0-rank spells.
all but my third can be applied to pve combat as well.