Unlike other games the emphasis in NetHack is on discovering the detail of the dungeon and not simply killing everything in sight - in fact, killing everything in sight is a good way to die quickly.
NetHack is a very deep and very fun game but also very, very challenging

Instructions
Use the keyboard for everything.
Use shift+? for in game help
You can use the number pad or hjkl keys for movement.
NetHack is a big game so it will take some getting used to.

For a complete description of the game and every command see the NetHack Guidebook

A Quick guide
Actions
Key - Action
? - help, documentation
/ - what is? (ask definition for something on the screen)
o - open something, use #loot for boxes and chests
s - search for secret doors (they are everywhere)
, - pick up things
ctrl-d or ctrl-s - kick (break open locked doors)
d or D - drop something
e - eat something
< or > - climb stairs
i - see what you are carrying, inventory
w - wield a weapon
t - throw/shoot
r - read something
a - use or apply (key, bag, pick-axe, etc)
z - zap a magic wand
Z - cast a magical spell
: - look what is here
. - wait a moment

Legend
symbol meaning
@ you (or a human)
. floor
< stairs up to the previous level > stairs down to the next level
+ closed door; spellbook
$ pile of gold
^ trap
% food, corpse, something edible (not necessarily healthy)
? scroll