Preparations are for the weak. Those who wish to seek enlightment must rely on their own resources. Such is the righteous path of the Glowing Guardian...
Unwinnable situations theoretically exist, however, given the sheer amount of options the game offers, it is almost always possible to win SOMEHOW. Unfortunately, due to the fact that there is a lot of things you don't know from the start, it is possible to make a mistake long before it becomes apparent that this mistake will kill you.
Nevertheless, unwinnable situations are more the realm of Purist Vicious dungeon runs. Pretty much everything else is usually winnable somehow.
The first thing you should do are not dungeons but class challenges. This is not because of rewards the class challenges offer, but because they are invaluable in learning the strenghts and weaknesses of your character. Knowing these is very, very cruical. Even bronze challenges tend to lie in the realm of "impossible" until you realise how to put the perks of your character to effective use. Once you've beaten a character's bronze challenge, you can probably use him effeciently in dungeon runs.
That being said, Fighter is one of the weakest classes, really. Try something else.
Also being said, some dungeons tend to be ridiculously hard for some classes. If you hit a roadblock, try another race-class combo.
Never spend too much time beating the same dungeon over and over again, too. I'm not sure how exactly this works, but if I ever lose a dungeon, I can nearly guarantee that my next attempt at it will be even worse. I only come back to the dungeons I've lost after several hours of rest and a few runs in different dungeons.
Being a mathematician surely helps. But it's not essential. I never use pen and paper - only my head and, in extreme cases, calc.exe. Also note that there are many things you can't calculate. Train your intuition - there are many cases where you should just wing it. Also be sure to make good use of Combat Prediction - it does a load of invaluable calculations for you on the fly.
Getindare effectively allows you to get one free strike against any monster that doesn't have a First Strike buff. Sometimes, that one strike might be enough to make a difference between epic victory or your blood being splattered all over the dungeon.
Do not use potions for any purpose other than slaying bosses, unless you are stuck in the dungeon and cannot proceed further. Seriously, don't. Even if you reach level 10(which is a tough feat by itself), bosses tend to be many times more powerful than you are, basically necessariating you to use some additional resources. Though it is very possible to beat some bosses without potions.
Keep playing, playing, playing, playing, playing, and playing repeated 20 more times over again. As said somewhere above, intuition is very useful - and the best way to train intuition is to keep playing and try different things at once.
Basically, here is the table of things you should learn for success, in order of what you should learn first:
1) Strengths and weaknesses of your class. Use class challenges for this.
2) Glyphs. They are of immense help if used properly, and most, if not all glyphs have some properties that look more like "tiny added bonuses", but instead are really the main reason to use the glyph at all. Figuring out various tricks with glyphs can be of huge use.
3) Experience management. It's a somewhat complex thing... What I've noticed about these forums, is that pretty much everyone suggests that you should never really fight monsters that are of the same level as yours or below. What I've found through experience is that this suggestion is not terribly effective. It's true that you shouldn't just run around and sword down everything that you are capable of swording down, but sometimes it IS very benefical to kill a monster of the same level, even if you are not doing this to spike a battle with levelup restoration. If you try too hard to maximize you experience gain, what you usually end up actually doing is running out of exploration space, not having enough experience to kill the boss, and not having enough resources to gain more experience.
Understanding when you should prey for monsters that are same or lower level than you and when you shouldn't is important, but rather hard. Intuition is your friend here.
That being said, if you suddenly notice that you can kill a monster that is of higher level than you, there is rarely a reason to not do so, unless it involves you exploring half the map for regeneration.
4) How monster regeneration works. Your own regeneration speed you can see if you hover your mouse over the health icon, for monsters, you have to calculate. Usually the amount of health they regain per explored tile is identical to their level. Double this for monsters with Fast Regen property, reduce it by 1 if the monster is currently on fire due to a fireball(hitting a level 1 monster with a fireball basically cancels it's HP regen). If monster is poisoned, his regeneration will work towards removing poison points first - monsters that regenerate faster are poisoned for lesser amount of time.
If you notice that you're able to deal damage faster that monster can regenerate, you can defeat higher level monsters this way relatively easily as long as you do not run out of blackspace. Which is nifty. I've randomly came up with a formula to quickly calculate this: multiply the damage of your melee attack by the amount of health you regenerate per tile, do the same for monster, and compare values. If your is higher, you can regen-fight it. Do note though that it has to be at least about 10-20% higher, otherwise, the battle will take too much blackspace out and leave you unable to defeat further monsters.
Also obviously note that this doesn't take into account glyphs and some status effects, because the formula for them gets too ugly. I usually just wing it in such cases.
5) Gods. In each of the four non-central dungeons you unlock first(eastern tundra, western jungle, etc.) there is a possibility to unlock two different gods by entering appropritate subdungeons and completing challenges. Some challenges are ridiculously easy(Jehora Jehey just requires you to step on his altar, getting OUT of that place, on the other hand...), others are ridiculously hard(oh bloody hell Tikki Tooki). Finally, the ninth god, the Pactmaker, unlocks automatically once you have all other gods unlocked. You should really work yourself towards unlocking all of the gods and learning how to use them - when used properly, gods can be of great help. By the way, unlike races, you do not have to survive the dungeon after completing the god challenge to unlock it - consider ruining your current dungeon run if you absolutely must do so to unlock a god.
Once gods are unlocked, learn them. You can do it either by completing puzzles that come with each god, or just by playing them in the dungeon and seeing what happens. They are also more or less well explained on the wiki.
That being said, there is a desktop dungeons wiki! It's rather incomplete and lies in several places,but hey, it DOES sometimes provide insightful advice.
I do not know if there is any IRC channel or something in similar vein for desktop dungeons, but I'd be actually surprised if there wasn't any. Consider finding it, and, if it exists, asking there for immediate help should some decision not be immediately obvious to you.
And finally. Preparations - especially the locker - is a force of truly incredible power if used properly. If all else fails, blow all your kingdom gold on preps! It will be worth it. I have never lost a heavily-prepared run so far.
Also, a tiny money-making trick - if you see that you cannot win the dungeon, do not kill yourself, and exit through the stairs instead. If you die, you will receive 0 kingdom gold from the run, if you will exit, all the gold you had + the gold value of your loot will be added to your kingdom gold. This will never be enough to compensate for losing all preps, but it's still a consolation.
Geez that is a bloody shipload of text.