It's about high time I got off my lazy ass started making TCG articles. I have a lot of stuff I know that I should teach, ever since the other person who knew WIXOSS pretty well isn't around anymore.
Before you try to do anything - make decks, play games, and so on - you should take a look at this article.
Attacking[]
The purpose of attacking Life Cloth is to win the game. Obvious, and you should do it whenever possible. No matter if you're the beatdown or the control, you should go after your opponent's Life Cloth whenever possible. Generally, you should not ignore Life Cloth to go after your opponent's SIGNI. SIGNI are disposable. Life Cloth are not. Not even if you're Midoriko and shitting out Repairs like the Lannisters shit gold.
But what is the purpose of attacking SIGNI? Not so obvious.
If you put a strong SIGNI in front of a weak SIGNI, then that weak SIGNI has already ceased to be a threat, even if you don't attack it with your strong SIGNI. Unless the weak SIGNI has a nasty effect like Valkyrie, Unforgettable Fantasy or Komaris, Phantom Beast, it becomes nothing more than a flimsy meat wall between your SIGNI and their Life Cloth, and if you don't attack it, your opponent might get rid of it themselves anyways to make space for more powerful SIGNI (through Main Phase trashing or Ener Charging it).
If you attack a SIGNI and get rid of it, then your opponent will probably replace it next turn. It's not particularly hard to replace SIGNI, especially non-valuable SIGNI like random level 1s. However... where is your opponent getting the SIGNI to replace those SIGNI from?
Basically, the main reason to attack SIGNI is to cause your opponent card disadvantage. If you keep attacking SIGNI, they'll eventually run out of SIGNI, leaving you with a clear path towards their Life Cloth... right?
Because players draw two cards a turn, as well as the many, many card advantage options available (Wake Up, Oversalvage, THREE OUT, etc.), it's very easy to generate SIGNI. Even if you only have a small card advantage engine, it is easy for games to become nasty attrition wars where both sides keep playing the full three SIGNI while having guards in their hand, and. Just. Won't. Go. Down. (This is especially evident if someone is playing Anne.)
Thus it is important to have finishers or wallbreakers - cards that let you get at your opponent's Life Cloth, such as removal or Lancer SIGNI. A finisher can be something as obvious as MEGA ULTRA SPOILER or Big Bang, or something as subtle as Code Piruluk Omega slowly whittling you down after discarding all your guards. Some decks, like Hanayo, Midoriko, or Remember, have more of these types of cards than others. We call them aggressive decks. Other decks, like Tama and Piruluk have less finishers than others, and focus on holding the enemy off until the late game by continually generating SIGNI through card advantage. I suppose you could call them control decks, because that's what they're analogous to.
Opening Hand[]
Unlike Hearthstone, mulligan strategies are simple in WIXOSS. In WIXOSS, there are very few tech cards, and cards are more suited to executing your game plan than hindering your opponent's. Besides, you don't get to see your opponent's LRIG until after you mulligan.
Like Hearthstone, you want to secure your early game with your opening hand. You want at least two level 1 SIGNI in your opening hand, and maybe a few level 2s. Spells that can generate SIGNI, such as THREE OUT or Get Bible, are also acceptable cards to be kept.
Normally, you should mulligan away all level 3 and 4s (other than Servants) and all spells that aren't relevant early game (such as BAD CONDITION or RAINY). If you don't have the level 1s you need, you should mulligan away most or all of your level 2s as well.
If you still don't have two level 1s, then you will have to just grit your teeth and take the damage, unless you have Thousand Punish or Haniel.
The First Three Turns[]
The point where players are at level 1 is the only time where both players are guaranteed to field less than the full three SIGNI. Therefore you should use this time to go after your opponent's Life Cloth.
If you're going first, you should play two level 1 SIGNI whenever possible, including Servants. That way, if your opponent also plays two level 1 SIGNI, they'll only be able to hit one of your Life Cloth. On your second turn you can then play the full three SIGNI, get rid of both of your opponent's level 1 SIGNI, and hit one of your opponent's Life Cloth, in that order. If you're going second, you should play two SIGNI, then hit one of your opponent's SIGNI and one Life Cloth, in that order.
But what if you can only play one level 1 SIGNI? Well, you should stop playing level 1 effect LRIGs. They suck. If you play only one SIGNI, you leave yourself open to losing two Life Cloth the next turn.
If you are using a limit 2 level 1 LRIG, and you only drew one level 1 SIGNI, then either you should have mulliganed harder for level 1s (mull harder), or you're just unlucky. Or... you should run more level 1s. Generally you should run 12-14 level 1 SIGNI, including Servants.
The Next Three Turns[]
Now that both players can field three SIGNI, the game generally becomes a shoving match, where one side pushes, then the other side pushes in turn.
Most players prioritize the use of utility SIGNI pre-level 4. Valkyrie, Helium, Hisui, MGT... the list goes on. Unless one of the players is running a very fast deck like Hanayo Ni Kai or Midoriko three-stop, the game usually isn't decided in these phases, so players usually build themselves up while holding off the opponent's token attempts at offense.
Vanilla SIGNI are perfectly fine, but they have a very specific use. Since vanilla SIGNI have higher power than average, SIGNI of the same level or below generally won't be able to attack them, so you won't need to spend a card to replace the SIGNI immediately. This isn't guaranteed though, especially if you go second.
Play three SIGNI whenever possible. You don't want holes in your Life Cloth before you're prepared.
You should always Guard whenever it is feasible. Often you will have to play a Servant as a SIGNI in order to protect against SIGNI attacks, and that's fine - it protects against one attack, just the same as if you had guarded with it, and it will end up in the Ener Zone instead of the trash (through being banished by an attack). Sometimes, you will need to let an attack through to secure enough ener to grow next turn, and sometimes you need the Servant you're holding in your hand to pay an off-color cost. But in general, guard if possible. Try not to let your Life Cloth be worn down to a point where you're vulnerable to finishers.
Generally decks run 8-10 Servants, but decks that disdain the presence of Servants, such as Urith5 decks, can run even less.
Level 4+[]
Level 4 is like pre-level 4, except the shoving becomes harder. At this point, your LRIG gets a proper effect and your SIGNI's effects become crazier.
Decks tend to run at least 8 SIGNI that are level 4 or above, and often even more. Level 4s represent the peak of your deck's power, and you don't want to run out of them quickly. If you run out, you won't be able to overpower the opponent's level 4s. Four level 4s is definitely too little. 6 is the bare minimum, and it works in decks that are heavily slanted towards the early game (but I'm not sure if you can pull that off well in a level 4+ deck).
Games tend to end through finishers, when a player wears the opponent down just enough so that opening a few holes in the enemy's SIGNI lanes allows enough attacks through to win the game. Otherwise, one of two things happen: either one player runs out of SIGNI to defend themselves with, or the game becomes a back-and-forth battle of attrition as described above. Always watch for your opponent's finishers. For example, if you know your opponent is about to grow to Hanayo Five, you'd better play some high-powered SIGNI so that her Exceed 
banishes only two SIGNI, and defend against the rest of the attacks with ARTS. If your opponent is playing Midoriko, you should predict the presence of Seiryu and Beiar, and make sure you don't go below 2 Life Cloth so you can take Seiryu's attacks when she comes.
LRIG attacks are generally an unreliable way to finish the game, unless you're Piruluk or using Arc Aura. Players often draw enough guards to stop nearly every single attack a LRIG makes. Players can and will run out of guards eventually, but it's slow-going, and by that time players will already have brought out their finishers. SIGNI attacks are much more reliable, even in the face of enemy Attack Phase ARTS.
TL;DR[]
- Level 1 is important. Always play two level 1 SIGNI on the first turn. Run 10-12 level 1 SIGNI.
- Level 2 and 3 somewhat important. Focus on utility.
- Level 4 is important. Run 8+ level 4/5 SIGNI.
- 8-10 Servants.
Next I'll be talking about each of the LRIGs' playstyles.