In order to fight your enemy you must know your enemy! You could just
choose to avoid all of the hostile mobs in Minecraft, but you can get things from that that are either hard or impossible to get elsewhere. So, before you venture out at night or into the dark depths of the caves, read up on your enemy and be ready to fight!

Step 1: Weapons and Armor

If you are going to fight monsters, you need to be properly prepared.

Crafting Weapons

1 Stick + 2 (Wood Planks | Gold Ingots | Cobblestone| Iron Ingots | Diamond) = 1 Sword
3 Sticks + 3 Pieces of String = 1 Bow
1 Stick + 1 Feather + 1 Piece of Flint = 4 Arrows

Armor

5 Ores (in an upside down "U") = Helmet
8 Ores (in all spots but top middle) = Chestplate
7 Ores (in large upside down "U") = Leggings
4 Ores (in two little columns) = Boots

Step 2: Creeper

Facts about Creepers:

Does not spawn in the light like other hostile mobs, but can survive in daylight
Is frightened off by Cats and Ocelots
Fights by exploding when within close proximity to the player
Will drop Gunpowder if it is killed (will not drop if it explodes)
Will drop Music Discs if it is killed by a Skeleton
Cannot walk over a rail on flat ground

Fighting a Creeper:

The best way to approach fighting a creeper is to hit it and back away. If you don't back up far enough fast enough, it will explode. If you back away far enough fast enough, it will not explode and will head towards you again giving you another opportunity to hit and kill it.
A safer way of engaging a Creeper is with a Bow and Arrow. Since you can only trigger a Creeper by being close to it, it won't blow up when shot with an arrow.
If a Creeper is in an area you do not want it to blow up in, lead it away specifically to water as possible as it won't cause damage in open water.

Step 3: Zombie / Zombie Villagers / Chicken Jockey

Facts about Zombies:

Will spawn in the dark and, unlike a Creeper, will light on fire in daylight
Most common hostile mob in the game
Fights by hitting you
Have variations including a Zombie Villager and Baby Zombie
Can spawn using weapons and wearing armor
Zombie Villagers can be cured with a potion
When killed, can drop the following; Most likely: Rotten Flesh; Rarely: Carrots, Potatoes, and Iron Ingots
Can pick up items you drop

Facts about Baby Zombies:

Will create a Chicken Jockey if it rides a chicken
Runs faster than normal Zombies
Won't burn in sunlight like normal Zombies
Can fit through 1 by 1 gaps

Fighting a Zombie:

Can be fought with any weapon. If attacking with a sword, you can stand one block above it and this will make it less likely that the zombie will be able to hit you as long as you continuously attack him until he is killed.

Step 4: Spiders and Cave Spiders

Facts about Spiders

Are a neutral mob when in higher light levels and are hostile when in a lower light level; so if you run into them at night, they will attack you; if you attack a neutral spider in daylight, it will defend itself and attack back
They look the same except the Cave Spider is blue and smaller than a normal spider
They do not burn up in sunlight
Cave Spiders are poisonous: the poison cannot kill you itself, it will only bring you down to 1 heart at most
They can climb up blocks vertically
While Spiders spawn naturally in the game, Cave Spiders only come from Monster Spawners from Mine Shafts
They can both drop String and Spider Eyes when killed
A Spider can form with a Skeleton on its back making a Spider Jockey
Can jump 2 or 3 blocks making them able to jump over fences which are 1.5 blocks tall
Cave Spiders are small than normal Spiders and are less than a block in width, length and height

Fighting Spiders

Like many of the monsters, it is easiest to attack them from a distance
For just normal Spiders: Fighting them face to face can be difficult since they jump around a lot, but because they are 2 blocks wide by 2 blocks long, you can dig a trench that is only 1 block wide and attack them from below and they won't be able to go down into the trench

Step 5: Skeleton / Spider Jockey

Facts about Skeletons:

Will spawn in the dark and will light on fire in daylight
One of the most common hostile mobs in the game
Fights by shooting you with arrows
When killed, can drop the following; Most likely: Arrows and Bones; Rarely: Bow
You can hide inside sugar cane from a skeleton
You can hide behind things to avoid being shot by arrows
Can wear head armor which will protect them from burning in sunlight
They cannot see you through vines
You can block their arrows with a sword

Facts about Spider Jockeys:

Is a skeleton riding a spider
Rarely appear
Both the spider and skeleton attack in their usual way (making them twice as deadly) and will need to each be killed
When killed, can drop the following; Most likely: Arrows, Bones, String, and Spider Eye; Rarely: Bow

Fighting a Skeleton and Spider Jockey:

The best and safest way to fight a Skeleton is a bow and arrow. When they get close enough to you, they stop walking and start shooting so when you try to run up to them to just hit them, they will continuously hit you with arrows
If going for a melee option, try to sneak up on them, coming at them from the site or above so you can hit them
Another option is to trick the skeleton into shooting another hostile mob, that mob will then attack the skeleton and they will fight each other
Lure them underwater and attack them from below, they won't/can't sink down to attack you

Step 6: Slime

Facts about Slime:

Appears as a green cube and when attacked, will break into smaller cubes
When small slimes are killed, can drop: Slimeballs
Usually spawns in layer 40 or lower, or in swamps (when spawning in a swamp, it will most likely need to be a full moon)
Can possibly spawn in any light level
Has 3 sizes: Large, Medium, and Small; you can run into any size Slime and only the smallest slime will drop anything when killed
Jump around to move

Fighting Slimes:

Use melee attack to attack Slime. It will break into smaller pieces. When those pieces are attacked, they turn into even smaller pieces. When you destroy those pieces, they die and do not continue to split up.

Step 7: Witch

Facts about Witches:

Spawn in Witches Huts which can be found in a swamp
Witches do not burn in sunlight
Look like villagers except for outfit, a wart on their nose, and a witches hat
When killed, can drop the following; Most likely: Glass Bottle, Spider Eye, Sugar, Glowstone Dust, Gunpowder, Redstone, or Stick; Rarely (when killed while drinking a potion): Potions of Healing, Fire Resistance, Swiftness and Water Breathing
Attacks with potions
Milk can be used to nullify effects from potions they use on you

Fighting Witches:

The best way to attack Witches is with a Bow from a distance out of range of their potions
If you don't have a bow, sprint at her and attack before she can do anything

Step 8: Silverfish

Facts about Silverfish:

Spawn when a Monster Egg is destroyed which will look like an ordinary stone block
When you attack them, other near Silverfish could be called to attack
If you leave it alone, it will crawl into another block making it a Monster Egg
Does not drop anything when killed

Fighting Silverfish:

Since the Silverfish is small and cannot climb or jump, it is safest to attack from atop a 2 block pole. Attacking it will draw other nearby Silverfish from Monster Eggs unless it is killed in 1 hit.

Step 9: Endermen

Facts about Endermen

Are found in the Overworld and The End
Are neutral but will attack you if you attack them or look at them; you can look at them out of the corner of the screen but do not look at their face
They will pick up/steal blocks they find
Can Teleport
Can drop Ender Pearl when killed
Take damage from water and rain
You can look at them through glass, while wearing a Pumpkin on your head or from a boat or minecart and not provoke them

Fighting Endermen

You can't provoke them just by looking at them if you wear a Pumpkin, it is wise to wear one when going to attack. Since they are tall, you can go into an area that is only 2 blocks high and attempt to attack from there.
Water is dangerous to them, fight them when they are near water and try to hit them in it. You can also stand in water and provoke it. It won't attack right away but it will eventually follow you into the water and take the damage. After attacking it will teleport away so try to kill it before it can do that.
Falling from a cliff can kill them since they cannot teleport while they are falling.

Step 10: Nether Mobs

The following mobs are only found in the Nether and are difficult to kill.

Beware!

Step 11: Blaze

Facts about Blaze:

Found in the Nether
Can fly and shoot fire charges
Not damaged by fire or lava
Besides being hurt by normal weapons, can be attacked with snowballs
When killed, can drop the following: Blaze Rods and Glowstone Dust
Very difficult mob to fight - attacks are unblockable and come fast

Fighting a Blaze:

Snowballs are a great method of attack as they do pretty good damage and you can throw them from a distance
Can use Wolves to fight, but they can be set on fire and die

Step 12: Ghast

Facts about Ghast:

Found in the Nether
Resistant to Water and Lava
When killed, can drop the following: Gunpowder and Ghast Tear
Does not go after a player, instead attacks from afar
Will open their mouth and eyes when attacking
You can deflect fireballs with arrow or melee attack (no weapon needed)

Fighting Ghasts:

Easiest to attack and kill with a bow and arrow
Deflect fireballs back at them to hurt and kill them
Can be attacked and killed with melee weapons, you can lure them closer with a fishing rod

Step 13: Magma Cube

Facts about Magma Cube:

Found in the Nether
Appears as a cube and when confronted, separates into 8 layers
When killed, can drop: Magma Cream
When killed, will release 2 to 4 smaller versions of itself
Is not burned by fire or lava

Fighting Magma Cubes:

The large Magma Cube is difficult to kill with just a sword, it is best to use a bow from a distance. Once it is broken up into smaller cubes you can more easily kill them with melee attacks.

Step 14: Wither Skeleton

Facts about Wither Skeleton:

Spawn in the Nether in Nether Fortresses
Are considered the Nether equivalent of a Skeleton; they look the same but are dark gray instead of light gray
Attack you with stone swords
Is not burned by fire or lava
Can pick up items and use them
When killed, can drop: Coal and Bone
When attacked, the Wither Skeleton will inflict the Wither Effect on you
Attack fast
If it gets a bow, it will shoot fire arrows at you

Fighting Wither Skeletons:

The best way to attack is a melee attack. Hit them and jump back out of the way. Repeat until you have killed them.
Can be shot with a bow, but they are fast and harder to hit than other mobs.

Step 15: Monster Spawner

A Monster Spawner is a 1 block sized cage that will spawn monsters. They will appear to have fire and mini monsters inside of them. They can be destroyed with weapon including: Pickax, Sword, and Ax.

Monster Spawners can be commonly found in dungeons which will be identified with Moss Stones and chests. They are also found in abandoned mine shafts.