Hangeul (한글) is the Korean alphabet. 한국어 is the Korean language.

I learned 한글 through the Korean Wiki Project. I also used an Android app called TenguGo Hangul when I didn't have access to my laptop.

There are fourteen basic consonants: ㄱ ㄴ ㄷ ㄹ ㅁ ㅂ ㅅ ㅇ ㅈ ㅊ ㅋ ㅌ ㅍ ㅎ
And five double consonants: ㄲ ㄸ ㅃ ㅆ ㅉ
A consonant is a speech sound or letter that is not a vowel.

There are eight basic vowels: ㅏ ㅐ ㅓ ㅔ ㅗ ㅜ ㅡ ㅣ
And thirteen "complex" vowels: ㅑ ㅒ ㅕ ㅖ ㅘ ㅙ ㅚ ㅛ ㅠ ㅝ ㅞ ㅟ ㅢ
Complex vowels are called diphthongs - a combination of no more than two vowel sounds.

I'll be listing all the characters and as close as you can accurately say them with roman characters, but the truth is, the only way to pronounce these characters correctly is to listen to them. Korean Wiki Project has audio clips for all the characters, I highly recommend you listen to their audio.

Consonants

ㄱ
k in skill, if at the beginning of a word
g if in-between vowels

ㄴ
n

ㄷ
t in stop if at the beginning of a word
d if in-between vowels

ㄹ
l at the ends of words and before consonants
flap r if in-between vowels

ㅁ
m
 
ㅂ
p in trap
b if in-between vowels

ㅅ
s
sh when combined with the vowel ㅣ,ㅑ,ㅒ,ㅕ,ㅖ,ㅛ,ㅠ

ㅇ
silent if in the position of a syllable. It is a placeholder because vowels cannot be written by themselves.
ng in sing if in the final (bottom) position

ㅈ
ch in match
dg in badger if in-between vowels

ㅊ
aspirated ㅈ, ch in cheek

ㅋ
aspirated ㄱ

ㅌ
aspirated ㄷ

ㅍ
aspirated ㅂ

ㅎ
h

Double Consonants

ㄲ
strong ㄱ

ㄸ
strong ㄷ

ㅃ
strong ㅂ

ㅆ
strong ㅅ
vowel combination rule still applies  (ㅣ,ㅑ,ㅒ,ㅕ,ㅖ,ㅛ,ㅠ)

ㅉ
strong ㅈ

Basic Vowels

ㅏ
a in art

ㅐ
e in dress

ㅓ
awe

ㅔ
a in face

ㅗ
straight o sound

ㅜ
oo in moon

ㅡ
eu

ㅣ
e in free

Complex Vowels (Diphthongs)

ㅑ
ya

ㅒ
yae

ㅕ
yaw
 
ㅖ
yea

ㅘ
wa
 
ㅙ
we

ㅚ
we

ㅛ
yo

ㅠ
yu
 
ㅝ
w-awe

ㅞ
we/wai

ㅟ
wi
 
ㅢ
eu-i