NetHack is sometimes portrayed as the mother of all hack'n'slay role-playing games where you walk across a level and kill everything in sight. But this gives only a partially correct description as NetHack has a lot more to offer and is still undergoing active development. In addition, NetHack enjoys a large fanbase of people who help new players with the first steps and offer extensive information and extensions to the game.
Several different frontends exist for playing NetHack, for example a Gnome or Qt variant. There exists even a seperate SDL frontend called Falcon's Eye, but the only version that will give you the true spirit of NetHack is the console interface, where all monsters and other dungeon features are displayed as colored ASCII characters. However, the gameplay is always the same: you start by choosing your character class, which defines the basic properties of your avatar. Obviously, a barbarian is much better than a wizard when it comes to brute force combat, however the latter is much more skilled in magic. Of course, there are some classes which are in between these two extremes.
Once you have chosen your class you will find yourself in the first level of the Dungeon of Doom. Your mission is to retrieve the Amulet of Yendor, a magical artifact that was stolen by the evil god Moloch. However, in the beginning you have very little to complete this task, as you are only equipped with a weapon, some armor, a small lunch packet and maybe a few other more or less useful things. If you wander around a bit, you will encounter the first dungeon inhabitant, which is probably a hostile monster. Now you have several options: you can hit the monster with your weapon, try to cast a spell in order to kill it, use an item to help you or just run away. Since NetHack is a turn based game, you have plenty of time to think about the many options the game offers you to (hopefully) solve a situation. The number of options increases strongly as the game advances and you have more items in your inventory. However, this also means that there are more and more ways to die quickly since the monsters will become stronger and the dungeon traps will become nastier.
If you survived the first few combats you can explore the level a bit. Most levels in Nethack are completely randomly generated, so knowing where the things were in a previous game won't help you in the present. If you stumble across an item on the floor that you have not seen before, it will usually carry an ambigous name, which means that you first have to find out what it is. This sounds easier than it is, because simply trying it out is probably the fastest way to die as many items can be very dangerous.
In the first levels you will find special rooms like shops where you can buy and sell equipment, and of course lots of monsters. Later on, there will be even special levels and additional levels seperate from the main dungeon. Most probably, you will die during the first few levels and there will be no savegame to restore. In this aspect NetHack is a very cruel game: if you save your game, NetHack will automatically quit and when you restore it, the file will be deleted. Of course, you could easily copy your savegame away before restoring it, but this practice is known as "save-scumming" among NetHack players and is considered as foul play. If you would like to avoid dying too quickly, you can play in the so-called "explore mode" but this also means that you won't make it into the highscore list. While this feature is often questioned by new players, it adds an extra thrill and leads to more careful planning of your actions.
If you are too impatient to discover the laws of the game by trial and error, there are extremely helpful lists and guides called "spoilers" on the net that will explain what will happen if you perform a certain action. However, most outcomes will be randomly calculated and while an action may result in a beneficial effect it can also ruin your character. In the spoilers you can learn a lot about the D&D-style game engine, too. If that doesn't please you there is always the source code to give a definite answer to your questions.
NetHack is a very addictive game. If you manage to survive the first few levels and advance your character you will spend a lot of time to dive deeper into the dungeons. To win the game — also known as to "ascend" — takes several days of playing time even for an experienced player. This playing time, however, is filled with excitement and fun, as there will always be new situations where something unexpected will happen. Only during the late midgame, when your character is fully equipped with all neccessary items and skills needed to win the game, the game can become slightly boring and result in stereotypical exploration of the levels. But this timespan is very small compared to the rest, and later on the game has to offer some more surprise ...
Even if you eventually manage to ascend, the game still has a lot more to offer. You can try playing a different character class, as this will usually require a different playing style and will lead to totally new game situations. The random nature of the levels ensures that there will be no old roads to follow — around each corner there could be the key to ascension or a sudden death. For more experienced players, there are different conducts to choose from in order to make the game harder and more interesting. For example, you can choose to never read or write anything, which means that there will be no spellbooks and no magic scrolls to benefit from. If that still sounds too easy, why not trying a foodless-atheist-polyless ascension (warning, spoilers follow)?
Contrary to what the name suggests, NetHack doesn't have a multiplayer mode. The name refers to the collaborative development model, not to a game feature. However, you can play it on one of the public game servers which will mean that your highscore will be prominently displayed and you will sometimes stumble upon the remains of another player's character. But be prepared since what killed him might as well kill you!
Anyway, if you have the slightest interest in role-playing games, you should definitvely give NetHack a try. For all others, Nethack is the best chance to enter the world of monster-bashing and magic.