Overivew
Fanatic is one of my favorite heroes both in terms of theme and game play. She's really quite a powerhouse of a hero, but like all heroes, she has her quirks. Her deck can be strange to play and seems to be a mix of straightforwardness and... not. With that said, Fanatic excels in both combat and support roles, but you must be aware of the state of the game to extract maximum benefit.
Fanatic Basics
Here are some things you absolutely must fully comprehend in order to get good use out of Fanatic. Fanatic is all about gaining maxiumum use out of buffs and debuffs. Keep track of your bonuses, always know if you are doing net increase in damage, net decrease in damage, or are breaking even.
Suppose you have a +1 damage bonus, what is better: using it once or using it 5 times? The answer is obvious, but you must keep this in mind always. Many Fanatic cards and abilities hit for small amounts of damage, this makes any +1 damage boost very effective for her. To be clear, Fanatic can often make better use of +1 damage than can, say, a hero like Legacy. Now granted that Legacy isn't known for being a combat powerhouse, but bear with me so I can illustate this point. If Legacy has +1 damage, he might use it twice on his turn, one from a one-shot, and once from motivational charge. This is being pretty generous, as Legacy only occasionally plays damaging once shots, and often does not have motivational charge out (or will choose to use another power instead). In Fanatics case, she essentially always "uses" +1 damage at least twice because of Exorcism. She has some buffs in her deck that she will play (Absolution) , but you can almost count on her playing a damaging one-shot every single turn, he deck is just full of them. So she will pretty much use +1 damage at least 3 times, and sometimes a whole lot more.
By the same token -1 damage (or +1 enemy armor) hurts you more than it might hurt your counterpart heroes. Knowing what to do when your attacks arent as effective is just as important as knowing what to do when they are. Try to do something better than just doing damage, this is a great time to buff yourself. You could lay down Absolution, Undaunted, or Aegis of Ressurection. Absolution is a card that very well might already be out, so if its not and you have it, play it. Absolution can definitely help because it can change your power phase from the 1+1 damage mode to a 3 damage power, which is preferable when enemies have armor. Practically no enemies except Matriarch's birds and some environment cards deal 1 damage. For this reason I usually do not play Undaunted unless on Pike Industrial or against Matriarch. It also has some applications on Atlantis because of the 5+ damage thing, but I tend to feel Undaunted is Fanatics worst card, and is very very situational. Aegis is a good play, but you typically want to play it just before you die, in case something comes up that kills your stuff. However, if not playing against a villain with equipment destruction, this can be a nice play when at -1 damage. Prayer of Desperation is also quite good in these situations if you have 4 or less cards when you play it (this makes it better than just drawing 2 cards for skipping play and power phase).
In the one-shot area, Divine Sacrifice can be used to get in irriduceable damage if you play using the Enhanced Edition. Just be careful who you use it against. Final Dive is another good card, often able to take down enemies that are providing Damage Reduction (like Gene-bound guards) opening the door for Excorcism and/or helping other heroes.
Negative damage is not always a liability that you must play around though. Namely, you can play Chastise and take less damage. Chastise is a very good card that can pull the teeth right out of some of the most threatening cards in the game. Embolden also benefits from heroes doing less damage.
Offense
Exorcism and Absolution are pretty straightforward, but Fanatic has a lot of offensive tricks. Smite the Transgressor is a very good play when doing +damage, 2 damage from the card, 1+1 from exorcism and 3 from Absolution means that you have just used your +damage buff 4 times. While I'm talking about powers, I should mention; I do not like Sacrosanct Martyr. I feel it is simply too self-destructive to be useful. 1-for-1 ratios of damage dealt per damage taken are not something you want to be doing too often. I will on occasion play this card anyway if something absolutely needs to die right now and there is no other way to do it. I feel Sacrosant Martyr should be reserved for desperation attacks though, and definitely not something you plan to do every turn.
Getting back to one-shots though, Brutal Censure and Sanctifying Strike should be your bread and butter. Fanatic needs to draw cards. She needs to draw a lot of cards. If you are at +damage or nueteral damage, you should pretty much always play one of these cards unless you have something that is much better.
Why do you need to draw cards? Well because you're looking for Wrathful Retribution, aren't you? The more cards you draw, the better your odds of pulling it. Usually play this as a finishing move on the villain, but has other applications like getting rid of Voss' dreadnaughts or Electro-pulse explosives. Sucks to lose it though, but if you have a hero that lets you get it out of your trash... good times.
However, there is another, better reason you need to draw cards; Divine Focus. You are twice as likely to get this card as you are to get Wrathful Retribution, so you can't dismiss it. Divine Focus is your other "nuke" card and to be quite honest, it is my favorite of the two. Strangely, this card is better if you have more heroes because you can use it more before having to pay the price, but it is a nice card no matter how many players. The key is that you can discard a card at the start of every turn for 2 damage. In a 4 player game, there are 6 turns per round, so you can deal 12 damage. This is very respectable, but you really should wait until you are at +damage, and as you stack on more +damage the card gets stupidly more effective. Each +1 damage essentially gets used 6 times by Divine Focus alone. So if you are at +1 damage you can deal 18, if you manage to drop this when you are at +2 damage, you can deal a whopping 24.... enough to rival all but the best Wrathful Retributions. I once had a game where even though I didn't have many cards in hand, I dropped Divine Focus turn 1 against plague rat with Fanatic infected and did a rediculous amount of damage thanks to Legacy having Inspirational Presence in his opening draw. 4 cards, but with each card dealing 6 damage, it was an easy 24, add on 10 more from an Excorcism and Plague Rat was 1/3 of the way dead just because of Fanatics first turn. I would say it is definitely "worth it" to play Divine Focus at +1 damage, but if you think you can hold out for +2 or higher, than go for it. This card can be highly efficient with damage buffs. If you can take the damage and happen to have enough cards or Prayer of Desperation in your hand... you can repeat the fun all over again on your next turn.
Support
While her primary role is combat, Fanatic has many good support cards. Chastise, Embolden, and Consecrated Ground are all pretty straightforward and nice to have. Zealous Offense can be quite good but it is tricky to use. It can be very difficult for Fanatic to deal at least 3 damage on her turn without her one-shot play for the turn (which your card play will be taken up by Zealous Offense). It also doesnt take effect until the round after you play it. So the best way to do this is to play the card out-of-turn, but with the exception of incapacitated powers and Argent Adept, this is quite difficult to do. So you may have to rely on having a +damage buff to get it out, or being neuteral on +/- damage and have Absolution. You can also use Sacrosanct Martyr to get the card out, but again, this is probably only if you're desperate, and if you're desperate, you probably cant wait a turn for Zealous Offense to take effect.
So we've come to End of Days... what a good card, and a very situational card. Although it can really own Akash-Bhuta from the Infernal Relics expansion, usually you dont want to destroy your stuff. Sometimes, you have to though, and End of Days can be a lifesaver against Forced Deployment or Electropulse explosive. It would be kind of funny to take Fanatic, Ra, and Nightmist as your team, because they are the characters with Relics, you could play End of Days and have only a minimal setback from the card. Unfortunately, Nightmist and Ra have plenty of ongoings they might want to keep around too, so it might not be worth it. The primary benefit of not destroying Relics is that you get to keep Absolution and Aegis of Ressurection.
"Redeemer" Fanatic
The Fanatic Promo card is quite interesting, I've not had a lot of time to play with it. It lets you draw a ton of cards and helps keep you healthy, but at the expense of Exorcism, which is a pretty hefty price. It helps Fanatic be good in situations where she might not otherwise excel, like against Voss or Omnitron where -damage is very common. You can build your hand easily towards Wrathful Retribution or Divine Foucs. Redeemer Fanatic seems to fill primarily a support role until you just explode onto the scene with your incredible hand. Would be pretty interesting to go around and Chastise everything or use Embolden on yourself, keeping your HP from dropping too fast with Redeem and maybe dropping an Aegis if your health got too low.
Particularly Rediculous combos
For some reason, a lot of Fanatics cards seem to be really abuseable if you have the right teams. Here are some good ones.
Fanatic+Legacy: Okay, who didn't anticipate this being first? How many times have I talked about how good Fanatic is with bonus damage? A lot. Its almost trivial to give Fanatic +2 damage boost with Galvanize and Inspirational Presence. So good for her entire deck, particularly Divine Focus though.
Fanatic+Unity: Bee Bot + End of Days. You can destroy what you want with End of Days, then kill off Bee Bot with EoD, and use its power to destroy EoD, leaving all the rest of your equipment and ongoings intact. The other combo is Chastise + Stealth Bot. You are now immune to practically all damage until something destroys ongoing cards. Fanatic must still take the self-inflicted damage from Chastise to keep the card in play, but it's a small price to pay for ignoring all other damage to all heroes.
Fanatic + Ra: This really seems like a match made in heaven/s. In addition to Imbue Fire really benefiting Fanatic, Embolden really benefits Ra, who can make excellent use of a second power per turn.
Fanatic+Visionary (thanks to Phantaskippy!) : They have a lot of synergy going on. Of course Fanatic loves to draw cards to fuel Divine Focus or maybe get a chance of picking up Wrathful Retribution, so Enlighten is great. But Twisting the Ether is another beast entirely. Fanatic benefits greatly from a twisting the ether because she can use the +1 damage buff a lot. However, turning her damage into Radiant damage can be great too, if you've got Sacrosacnt Martyr. If you manage to turn the damage from Divine focus or Chastise (or both!) into Radiant, suddenly the Sacrosanct Martyr power looks a lot more attractive. If you had Divine Focus up, you could attack yourself for only 1 radiant damage, and still be able to belt out 6 damage with Sacrosanct Martyr.
Wrapping Up
Hope you have enjoyed my guide, let me know if there is anything that needs mentioning. I find Fanatic an extremely fun and powerful character to play, I hope these insights will lead you to feel the same way.