First off, this is my first guide. Hopefully you find it useful. I'm far from the best Desktop Dungeons player, but I think I'm pretty well qualified to offer some advice on the beginning game.

Now, the first rule of Desktop Dungeons is We never, ever fight anyone at the same level as us! Say it with me now. No, don't say it, shout it! Make your neighbors think you're weirder than they already do! Write it on your hand in black sharpie, I don't care but whatever you do don't forget the first rule. Never fight a monster at the same level as you! I'm going to keep coming back to this point, and the entire purpose of this guide is to teach you the basics of how to tackle enemies that are higher level than you.

First off (er second), Big thanks to Jay Plays Games on Youtube. If you feel up for watching some videos on Desktop Dungeons his tutorial series is a great place to start. He covers a lot of the same ground as I do here and does so with a soothing voice and pleasant visuals that I lack.

Also a big shoutout to the contributors to the desktop dungeons wiki. Wouldn't have gotten this done without it open in another window.
http://www.qcfdesign.com/wiki/DesktopDungeons/index.php?title=Main_Page

Resources
Ok first thing you need to realize is that everything in Desktop Dungeons is a resource. In addition to the 'traditional' resources of most RPG's like Health, Mana, Glyphs (spells) and Items there are a few additional ones.

First and foremost is exploration. Each tile you explore lets you recover 1 point of mana and your level worth of health. You need to be careful with exploration though because as you explore any enemies that have been previously damaged regenerate their level worth of health. Exploration and regen fighting is an essential tactic to master when you are fighting monsters above your level.

Second is monsters. Monsters are a resource because they give you XP. XP means levels, and levels mean moar powar! Monsters can even heal you through a technique called "mid fight leveling" or "popcorn bowling" which I'll explain later on.

Third is levelsups. Yes, leveling up is a resource. Not only do you get more powerful overall (boost to attack and health) but your health and mana is totally restored, and you get rid of any nasty side status effects like Mana Burn, and Poison. If you can try to 'save' your levelups for when you are going to recover something from them. Don't kill some goober who isn't going to damage you anyhow just to push yourself over the XP line when you're at full health and mana, it's just a waste.

Know your Fight
Other than the dungeons themselves there is very little randomness in Desktop Dungeons. There are a few things like Dodge Chance, but 99% of the time you will know the outcome of a fight before you even begin. When you mouse over an enemy you can see exactly how much damage you will do to him, and exactly how much damage he will do to you. Same with spells. You will see exactly how much damage they will do. Use this! Plan your fights in advance. Don't just start clicking.

So there are 10 different races in Desktop Dungeons. For the purposes of this guide I'll be concerning myself with 5 of them. Racial bonus only really factor into conversion. Basically this means that when you drag an item or glyph onto the conversion symbol you get a certain number of points. Those points get translated into different things depending on your race.

Humans
You know em, you love em, they show up everywhere. Humans get +10% attack for every 100 conversion points. This makes them fantastic fighters since their basic damage will skyrocket if you find junk to convert. Keep your eyes peeled for anything that boosts your base attack value (adds +X to attack) as the humans % increase makes them much more valuable.

Elves
You wanna spam burnderaz? An elf is your man. You get an extra point of mana for every 70 conversion points. If you convert as you go this can be beastly. I've had elf mages get upwards of 30 mana which is enough for a blistering barrage of 6 fireballs.

Dwarves
Dwarves get an extra point of health for every 80 conversion. This is of limited use, since your health heals at the same rate as everyone else when exploring, which is your primary method of healing. That said health potions are particularly useful for dwarves, especially if you are playing as a priest (with the priest's health bonus) when they heal 100% of your health.

Halflings
80 conversion for a health potion. Useful if you plan on downing a lot of gummy berry juice (those were red right?). The benefits of a halfling priest are pretty obvious, while another good class is the Thief since thieves also get mana recovered when they drink a health potion. Halflings (and Gnomes below) are great races to go 'nova' on a boss at the end since you can spam potions like nobody's buisness and keep a fight going for a lot longer than you normally could.

Gnome
Just like a halfling except 90 conversion gets you a mana potion. Like halflings they make good thieves, but rather than priest you should be busting out the tomes of knowledge and go for a wizard. If you have 15 mana you can get off 3 burnderaz to begin with plus one more for each potion you drink. Start converting everything but your burnderaz and you will be able to get off 7 or 8 fireballs in a chain. Not much can stand up to that.

Ok so there are a lotta classes. 18 in total. I'm gonna look at the first 4 you're going to come across. The Fighter, The Priest, the Thief, and the Wizard.

Fighters:
Fighters have two big advantages plus one rather worthless one.

First, they gain an extra experience point for every monster they kill, and it costs 10% less for them to level up. The benefits of this should be obvious. Faster XP gain means faster level advancement, which means faster boss killing. It also lets them leave more 'popcorn' scattered about behind them which is supremely useful when level up fighting.

Second is their death protection. Sometimes that one extra hit is all it takes to kill a boss and go riding back to town. Save it for when you absofragginglutely need it.

Third is their ability to see all monsters of their level or lower in a level. Meh. You don't want to be fighting guys at the same level as you anyhow so this is pretty useless.

Don't overlook glyphs as a fighter. Getinder and Byseps are obviously useful both for starting and finishing fights, but Pisorf is a surprisingly potent direct damage spell in the hands of a skilled fighter, since it does damage based on your attack power rather than your level like Burndayraz.

Priests
Priests are surprisingly tanky guys. Don't treat them like a spell caster, get in and mix it up. All three of their advantages focus on the bashy bashy side of combat.

First they get an extra 3 hitpoints per level up. This is very useful at low levels as most of the monsters are designed to juuust barely kill you before you kill them. This means you can get an extra swing in and come out singing.

Second they get 100% healing from health potions. This is good towards the endgame If you can tank 2 hits from a boss monster that means that every healing potion is effectively 2 free hits.

Third they get a bonus of 150% damage to undead. If you see a dungeon that has a zombie or a wraith as a boss monster this is killer.

Wizards
Shazam! Like every other game in existence wizards are comparably squishy, but they can unleash massive amounts of damage. Wizards are one of the most powerful of the 4 starting classes, but you need to be careful with them

First they get a free burndayraz glyph at the start of the dungeon. This is sweet. You have a way of zapping things without getting your precious skull smashed in. Glyphs are also small items, so you can cram more of them in your inventory. They also deal 2 burning stacks to a monster when they use burndayraz, but using that well is a more advanced tactic that I'm not going to delve into here.

Second all of their glyphs cost 1 less mana to cast. This means that considering you start with 10 mana you can cast burndayraz twice. Combined with a single attack this is enough to kill, or seriously weaken most level 2's right from the get go. They also boost your other conversions by 10 points.

Third they see the locations of all the glyphs on the map. This is handy because it is a useful way to guide your exploration. Go in the general direction of the glyphs.

Thieves
The most difficult of the starting classes to play well thieves work best as a hybrid fighter/mage.

First and most useful is that there is no difference between a health and a mana potion to a thief. They both work just as well. This lets you burn potions to hit things and zap them at the same time.

Second they also get 33% more items on a map, by items the game means extra potions, and extra attack/health/mana boosts. This is pretty damn useful. The boosters are universally useful, and thieves are pretty efficient potion drinkers so unless you're going for parched, the extra potions are pretty damn handy.

Third they do an extra 30% damage to an enemy with full health. Take advantage of this to beef up your attack score as much as possible with byseps before hitting someone. Not a huge advantage, but it helps sometimes.

So if you're still with me, congratulations! We're about to hit the most important part of the guide, how to fight above your level.

First things first. Never, ever under any circumstances fight a monster of the same level as you... Madness you say? Hardly, and here's why.

If you are fighting a monster of lower level than you, you get XP equal to their level, and you also get first strike against them. This means you can use low level monsters as an easy way to level up when you need to. Leveling up totally restores your health and mana so it is a critically important resource to use.

If you are fighting a monster above your level they hit you first, but you get bonus XP depending on how big the level gap is. For normal difficulty dungeons you are normally fine with fighting enemies one level above you, but these same techniques will work for monsters 2-3 levels higher than you as well, and the XP bonus's (boni I dunno) are that much better.

Now if you are foolish enough to fight a monster of the same level as you not only do they get first strike on you, but you also don't get any bonus XP. Boooo.

Now, how to do this.

First things first, at the beginning of a dungeon don't try taking on monsters more than one level above you. Tackling a monster who is 2-3 levels above your own generally requires resources like items or tile powerups that you don't have available at the beginning. Don't start eyeing those guys until you're around level 4 or so.

One of the simplest techniques that requires the fewest resources only needs a burndayraz and the ability to cast it twice. If it isn't obvious the Wizard is tailor made for this as he starts with burndayraz and enough mana to cast it twice.

The fight itself is simple enough. Hit your enemy once, cast burndayraz twice. If he isn't quite dead, check and see how much damage he does to you and go explore enough tiles (and exactly enough tiles) to raise your health to one point above his damage. Win.

This works for other classes who get burndayraz early too. Hit once, cast burndayraz, go explore two tiles, cast burndayraz again and hit again.

If you get your hands on burndayraz and getindare then you can chain a hit, two fireballs and a second hit after casting getindare since first strike overpowers the first strike from the monster.

Regen fighting

This is a more advanced technique that can be used to tackle monsters 2-3 levels higher than you that relies on either a willingness to experiment (please experiment), experience, or really liking math. Find an enemy that you can survive at least one hit from. Use the hit burn burn combo and then go explore a bit. As soon as you can either survive another hit, or fire off another burndayraz go in and do it. If the enemy has regened more than half of the damage that you just inflicted on it then chances are good that either you arn't going to be able to kill it, or you're going to waste so much exploration killing it that you'll hamstring yourself in the long run. Alternatively you could likely win with a couple potions, but generally you want to save those for boss fights.

Mid-Fight levelups
This is a great technique, particularly useful with bosses, but only really useful if you are fighting something at least 3 levels above you. If you need to levelup fight to take on a guy 1 level above you then you'll be killing him when you are at the same level (and what did we say about fighting guys at the same level as you?) or just one level above you which is a bit of a waste of a levelup.

Now to levelup fight you want to get yourself to a point where you are within 1 or 2 (or 3) XP from leveling up. Be careful getting to this point with a fighter, remember that you gain an extra XP from every monster kill. My forehead has met my keyboard a few times because I forgot that and wasted a levelup.

Now go and bash away at your target. You can regen fight a bit, but be careful as higher level monsters will regenerate a lot faster than you can damage them. If you need a tile or two to get an extra burndayraz or hit in that's fine, but don't explore more than that. Ideally you want to be as low on both health and mana as possible.

After that find one of the pieces of 'popcorn' you've left scattered about the dungeon. This is the biggest reason we've left those monsters kicking around is for this exact scenario. Find something you can kill in one hit. Kill it. Level up. Now when you mouse over your main target you'll see he hasn't healed at all. Go in full bore and you should be able to finish him off for mad XP.

Generally speaking I will use a potion or two if necessary to fight someone 3-4 levels above me. The XP is worth it.