There is an overworld in DD, but the main action happens in each dungeon run that’s usually single screen and takes about 20 minutes to complete. The screen is roughly a 20x20 grid and your character can only see the 8 squares around him. You can walk as far as you want through the dungeon without anything happening, as long as your path isn’t blocked by a monster or a wall - the game is turn based and things only happen when you attack or cast a spell or similar (e.g. when you attack a monster it attacks you back). However, the way you regenerate health and mana in this game is by exploring squares that you haven’t previously seen, so you usually don’t want to explore just for the sake of exploring.
You start at level 1 in each dungeon run and can gain XP by killing monsters. Each time you level up you gain more max health and attack damage (and some abilities are based on your level, like the damage dealt by your fireball spell). Monsters also range from level 1 to 10, and to win the dungeon run you have to kill the boss who is usually the only level 10 monster and is much stronger even proportional to its level than other monsters. Each monster grants XP equal to its level, but if you kill a monster higher level than you, then you gain bonus XP equal to double the level gap. You soon figure out that the best thing to do is look for monsters that are just 1 level higher than you.
You don’t start off with any spells in each dungeon run, but can find them in the dungeon. Spells can do things like grant you first strike (so if you land a killing blow on the monster it won’t hit you back) or deal magic damage to the monster that doesn’t let it attack back, or destroy walls, or give you more xp for kills, etc. You can also find piles of gold, which let you find shops that you can buy items from that increase your damage or max mana etc. You can find altars of gods who you can worship, who reward or punish you for taking certain actions and you can spend piety to get benefits from them.
The lack of spells at the start feels like a runner without their icebreakers. You can only kill weak monsters without having spells to let you deal extra damage without getting hit back. You can click to draw through your deck (i.e. use up exploration space) to find the spells but that could cost you the ability to regenerate later in the game.
The two main things that make DD strategic are using the combinations of abilities, monster abilities and game mechanics to let you kill things, and resource management. For example, you can start fighting a big monster, then while it’s half dead you can go kill some smaller monsters to level up which restores all your health and mana, then go back and finish off the big monster. Or you could explore while fighting a big monster, but that lets the monster regenerate health during the fight too - so it’d only be worth it if you’re doing more damage than it is doing to you, assuming you have the same regen speed. But there are also strategies that are less like using corroders on fire walls and more like gang sign Leela decks - wizards who can rely entirely on their fireball and rogues who try to max out first strike damage and dodge chance.
There are ways you can lose a dungeon run and be forced to retreat or die, apart from just misclicking on a monster that was too strong at the wrong time which can unfortunately happen.
You could run out of exploration space. This could either be thought of like a runner who can’t draw from their deck due to thousand cuts PE/PU, but it is also similar to a runner who takes too long to set up their rig and has no time to stop the corp scoring their agendas.
You could run out of health potions while fighting the last boss. This is like a runner who needs to get into a remote to contest the last agenda but runs out of credits.
You could get locked out by a boss that you can’t even hit once regardless of how many potions you have or by the geography of the dungeon trapping you in a spot you can’t walk out of. This is like a runner with fixed strength breakers / Aumakua who has no way of dealing with a specific ice.
You could get debuffed by fighting normal monsters while trying to level up, leaving you not strong enough to finish the run, like a runner who facechecks too much and loses their resources and breakers.