Basic Moves:

Moves that require only a button press:

HIGH PUNCH - Produces a punch to the face. Many can be strung together in succession by rapidly pressing the button.
LOW PUNCH - Your character will punch the opponent's midriff. Many can be strung together in succession by rapidly pressing the button. Not as powerful as a high punch but can hit the opponent while they are ducking.
HIGH KICK - Smacks your opponent in the face with a powerful kick
LOW KICK - Not as powerful as the high kick but a little faster to recover, kicks the opponent in the abs.
BLOCK - Blocks attacks

Combination Moves:

Moves that require a button to be pressed simultaneously with a direction:

Jump Kick - Jump + either KICK button.
Jump Punch - Jump + either PUNCH button.
Pressing up plus kick or punch will result in your character punching or kicking in midair without moving in a direction. If jumping towards or away from the opponent, pressing punch or kick will cause your characrter to extend their limb a little further to hit the opponent and will cause more damage. A Jump Kick is more powerful than a Jump Punch, but Jump Pucnhes are better for winning aerial battles.
Uppercut - Down + HIGH PUNCH.
The most damaging normal move in the game - This will send your opponent soaring into the air. Unlike the original, where you could press either punch to execute the move, the uppercut can only be executed in Mortal Kombat II by pressing Down and High Punch.
Sweep - Back + LOW KICK
Sweeping knocks your opponent onto their back by tripping them over.
Roundhouse - Back + HIGH KICK
Your character spins around and gives your opponent a heavy kick to the side of the head. Unlike the original, Roundhouses in Mortal Kombat II send your opponent flying across the screen. Like the Uppercut, this move is also very damaging.
Weak Kick - Down + LOW KICK
Not really useful unless your opponent is ducking and avoiding your other attacks...weak and slow.
Throw - Forward + LOW PUNCH
Must be standing right next to your opponent. Different characters throw in different ways, but all throws do good damage. Throws cannot be blocked normally.
Block Throw - BLOCK + diagonally down + away
Pressing down and away while blocking will prevent your opponent from executing a throw.
Death Punch - Standing punch when opponent is jumping towards you.
Timing is the key...this move is pretty difficult to pull off, but when you can do it, it is VERY damaging.
Power Hit - Forward + HIGH PUNCH
Some characters elbow, some headbutt, but the basic premise is the same - a strong hit to the opponent in close quarters.

Special Moves:

Moves specific to each character that must be done with a combination of buttons and directions.

Johnny Cage:

Low Green Flame - Down, Down Forward, Forward, LOW PUNCH
High Green Flame - Down, Down Back, Back, HIGH PUNCH
Shadow Uppercut - Back, Down, Back, HIGH PUNCH
Shadow Kick - Back, Forward, LOW KICK
Nutcracker - LOW PUNCH + BLOCK simultaneously

Pit Fatality - Down, Down, Down, HIGH KICK 
Rip in Half - Down, Down, Forward, Forward, LOW PUNCH (Close)
Decapitate - Forward, Forward, Down, Up (Close - Helps to hold BLOCK)
Triple Decapitate - Down + LOW KICK + BLOCK + LOW PUNCH (Close - after performing the regular decapitate)                  
Babality - Back, Back, Back, HIGH KICK                             
Friendship - Down, Down, Down, HIGH KICK

Kung Lao:

Hat Throw - Back, Forward, LOW PUNCH (Press Up or Down to control hat)
Spin Attack - HOLD BLOCK, Up, Up, release BLOCK, press LOW KICK rapidly
Teleport - Down, Up
Torpedo Kick - Down + HIGH KICK while in air

Pit Fatality - Forward, Forward, Forward, HIGH PUNCH
Hat Split - Forward, Forward, Forward, LOW KICK (Sweep Distance)
Decapitate - Hold LOW PUNCH,  Back, Forward (then aim hat at head - Far Distance)
Babality - Back, Back, Forward, Forward, HIGH KICK                          
Friendship - Back, Back, Back, Down, HIGH KICK                    

Liu Kang:

High Fireball - Forward, Forward, HIGH PUNCH
Low Fireball - Forward, Forward, LOW PUNCH
Bicycle Kick - Hold LOW KICK for 4 seconds, release
Flying Kick - Forward, Forward, HIGH KICK

Pit Fatality- Back, Forward, Forward, LOW KICK
Cartwheel - 360 degree spin away from enemy (Anywhere)
Dragon Morph - Down, Forward, Back, Back, HIGH KICK (Close)
Babality - Down, Down, Forward, Back, LOW KICK                         
Friendship - Forward, Back, Back, Back, LOW KICK

Baraka:

Blade Spark - Down, Back, HIGH PUNCH
Blade Slice - Back + HIGH PUNCH simultaneously              
Blade Fury- Back, Back, Back, LOW PUNCH

Pit Fatality - Forward, Forward, Down, HIGH KICK
Impale - Back, Forward, Down, Forward, LOW PUNCH (Close)
Decapitate - Back, Back, Back, Back, HP (Close)                             
Babality - Forward, Forward, Forward, HIGH KICK                             
Friendship - Up, Forward, Forward, HIGH KICK (Helps to hold BLOCK)

Scorpion:

Spear Throw - Back, Back, LOW PUNCH
Teleport Punch - Down, Back, HIGH PUNCH
Scissorkick - Down, Back, LOW KICK
Air Throw - BLOCK while in air

Pit Fatality - Down, Forward, Forward, BLOCK
Incinerate - Up, Up, HIGH PUNCH (Half-screen away, helps to hold BLOCK)
Toasty Incinerate - Down, Down, Up, Up, HIGH PUNCH (Anywhere - Helps to hold BLOCK)
Neck Slash - Hold HIGH PUNCH, Down, Forward, Forward, Forward, release HIGH PUNCH  (Close) 
Babality - Down, Back, Back, HIGH KICK                             
Friendship - Back, Back, Down, HIGH KICK

Kitana:

Fan Lift - Back, Back, Back, HIGH PUNCH
Fan Throw - Forward, Forward, HIGH PUNCH + LOW PUNCH together
Fan Slice - Back + HIGH PUNCH simultaneously
Teleport Punch - Forward, Down, Back, HIGH PUNCH

Pit Fatality - Forward, Down, Forward, HIGH KICK
Decapitate - BLOCK, BLOCK, BLOCK, HIGH KICK (Close)
Kiss of Death - Hold LOW KICK, Forward, Forward, Down, Forward, release LOW KICK (Close)
Babality - Down, Down, Down, LOW KICK                
Friendship - Down, Down, Down, Up, LOW KICK             

Raiden:

Electric Shock - Hold HIGH PUNCH for 3 seconds, release
Torpedo Launch - Back, Back, Forward
Lightning Bolt - Down, Forward, LOW PUNCH
Teleport - Down, Up

Pit Fatality - Up, Up, Up, HIGH PUNCH (Helps to hold BLOCK)      
Electrocution - Hold LOW KICK, press LOW KICK + BLOCK rapidly (Close)     
Super Uppercut - Hold HIGH PUNCH for 7 seconds, release (Close)
Babality - Down, Down, Up, HIGH KICK (Helps to hold BLOCK)                             
Friendship - Down, Back, Forward, HIGH KICK                           

Reptile:

Acid Spit - Forward, Forward, HIGH PUNCH
Force Ball - Back, Back, HIGH PUNCH + LOW PUNCH together
Invisibility - Hold BLOCK, Up, Up, Down, HIGH PUNCH
Slide - Back + BLOCL + LOW PUNCH + LOW KICK simultaneously

Pit Fatality - Down, Down, Forward, Forward, BLOCK
Head Devour - Back, Back, Down, LOW PUNCH (Half-screen)
Invisible Death - Forward, Forward, Down, HIGH KICK (Close - while invisible) 
Babality - Down, Down, Back, Back, LOW KICK                          
Friendship - Back, Back, Down, LOW KICK

Shang Tsung:

Flaming Skull - Back, Back, HIGH PUNCH
Double Flaming Skull - Back, Back, Forward, HIGH PUNCH
Triple Flaming Skull -  Back, Back, Forward, Forward, HIGH PUNCH
Liu Kang Morph - Back, Forward, Forward, BLOCK
Johnny Cage Morph - Back, Back, Down, LOW PUNCH
Baraka Morph - Down, Down, LOW KICK
Kung Lao Morph - Back, Down, Back, HIGH KICK
Sub-Zero Morph - Forward, Down, Forward, HIGH PUNCH
Reptile Morph - Hold BLOCK, Up, Down, HIGH PUNCH
Raiden Morph - Down, Back, Forward, LOW KICK
Kitana Morph - BLOCK, BLOCK, BLOCK
Scorpion Morph - Hold BLOCK, Up, Up
Mileena Morph -Hold HIGH PUNCH for 2 seconds, release
Jax Morph - Down, Forward, Back, HIGH KICK

Pit Fatality - Hold BLOCK, Down, Down, Up, release BLOCK, Down        
Soul Stealer - Up, Down, Up, LOW KICK (Close - Helps to hold BLOCK)
Body Explosion - Hold HIGH KICK for 3 seconds, release (Sweep Distance)     
Kintaro Morph - Hold LOW PUNCH for 25 seconds, release (Sweep Distance - begin holding down before end of round) 
Babality - Back, Forward, Down, HIGH KICK                             
Friendship - Back, Back, Down, Forward, HIGH KICK

DEAD POOL FATALITY FOR ALL CHARACTERS: Hold LOW KICK and LOW PUNCH then Uppercut your opponent while holding the buttons.

Secrets:

Mortal Kombat II has three hidden characters: Jade (a female Ninja), Smoke (a male Ninja) and Noob Saibot (basically just a shadow)

To Fight Jade:

You must be in single player mode. Fight your way up the ladder until you reach the match before the question mark. When you are fighting in this match (the one before the question mark) use ONLY the LOW KICK button and win one round, and you will be sent away to fight Jade in Goro's Lair.

To Fight Smoke:

Must be playing on The Portal Stage (can be either single or two-player mode). Occasionally when you perform an Uppercut or another good move, Dan Forden will pop up in the corner and say "Toasty!". When he does, press Down and the START button simultaneously and you will be whisked away to fight Smoke in Goro's Lair.

To Fight Noob Saibot:

You must win 50 matches in a row (earn 2 Gold MK's) and you will earn the right to fight Noob Saibot. Obviously this needs to be in two-player mode, and you can have as many goes at beating him as you like as long as you keep winning the match after fighting him. (If you lose you will need to win 50 times again.)