The Korean alphabet, called in English letters Hangul (the u is actually equivalent to a Russian ы, or an American i as in sin, thus proving the stupidity of American romanizers), is known for being the simplest major writing system of China/Japan/Korea/Vietnam. I myself tried to learn it for three days, finishing learning it only on the third. Contrary to many people’s impressions, I did not find learning it particularly easy for an alphabet, partially due to the many muddled descriptions of the Korean sounds out there online. I found it notably harder than the Republic of China’s 注音 script for phonetically spelling Mandarin (though it’s only used as a guide for pronouncing the characters, rather than as a replacement for the characters themselves). Thus, I wrote a guide to make learning the script for English speakers easy.
The Korean alphabet has (by my count) 33 letters representing individual sounds. There are also seven more digraphs for vowel clusters and eleven more digraphs for consonant clusters, which I will not cover, but are extremely straightforward byproducts of the other letters. There is a complete list of Korean syllables here, which is useful for typing into Google Translate and flash cards.
ㄱ -this is the letter k, but is pronounced g if preceded by a consonant. This consonant is voiced (i.e., with the vocal cords moving during pronunciation).
ㄲ -this is the letter g, but unvoiced. Same as Mandarin g (as 过).
ㄴ -this is the letter n.
ㄷ -this is the letter t, but is pronounced d if preceded by a consonant. This consonant is voiced.
ㄸ -this is the letter d, but unvoiced. Same as Mandarin d (as in 的).
ㄹ -mixture of l and r.
ㅁ -this is the letter m.
ㅂ -this is the letter p, but is pronounced b if preceded by a consonant. This consonant is voiced.
ㅃ -this is the letter b, but unvoiced. Same as Mandarin b (as in 不).
ㅅ -Unvoiced “s”.
ㅆ -Voiced “s”.
ㅇ -stands for “ng” when a final consonant in a syllable, no sound otherwise.
ㅈ -Generally romanized as “j”, but in fact more comparable to a voiced Mandarin “c” (i.e., the consonant cluster “ts”) as in 词 and a voiced Mandarin q as in 去. However, unlike in these Mandarin consonants, where, according to the commenter Davenport below, “the tip of your tongue touches right behind where your upper front teeth meet the gum ridge”, “in ㅈ and the related consonants, the flat middle of your tongue touches the roof of your mouth”.
ㅉ -Similar to Mandarin z as in 子 (i.e., the consonant cluster “ds”) and j as in 就.
ㅊ -Similar to Mandarin c as in 词 and q as in 去. This consonant is unvoiced.
ㅋ -stands for the consonant cluster “kh”. This consonant is unvoiced.
ㅌ -stands for the consonant cluster “th” (not the English phoneme made by these letters). This consonant is unvoiced.
ㅍ -stands for the consonant cluster “ph” (not f). This consonant is unvoiced.
ㅎ -this is the letter h.
ㅏ -this is the letter a.
ㅐ -this is the letter “e”.
ㅑ -extra horizontal stroke on a vowel letter indicates a “y” before that letter. So “ya”.
ㅒ -See the principle behind ㅑ.
ㅓ -English “uh” sound. Same as Mandarin e as in 的.
ㅔ -same sound as “ㅐ”
ㅕ -See the principle behind ㅑ.
ㅖ -See the principle behind ㅑ.
ㅗ -“o” sound. Russian о.
ㅛ -See the principle behind ㅑ.
ㅜ -“oo” sound. Russian у.
ㅠ -See the principle behind ㅑ.
ㅡ -i as in “sin”; Russian ы.
ㅣ-“ee” sound. Russian и.
The final consonant of a Korean syllable is often silent. There are a lot more pronunciation rules in Korean than implied by the letters of the alphabet (e.g., ㄴ is sometimes not pronounced ㄴ in some words; some consonant clusters are sometimes not pronounced as consonant clusters); the quickest way to learn them is, in my opinion, to enter Korean words you see into Google Translate and listen to the sounds they make. Once you’ve listened to enough such sounds, you’ll remember the pronunciation rules.
It may seem silly, but a good way to get Mandarin phonetics down is to watch/listen to Pinyin alphabet songs for kids. There are many on Youtube. Once you learn the tongue/mouth positions associated with the Pinyin initials and consonants and listen to the kids' songs a bunch of times, Mandarin phonetics becomes very easy.
For example, these songs usually start by covering all the initials (the consonants plus y and w) beginning with "bo, po, mo, fo". The initials are clustered according to how they're pronounced with the same tongue/mouth position i.e. bo po mo fo are all pronounced using the lips hence they're labials and clustered together (bo po mo use both lips; fo of course uses the top teeth and bottom lip, just like English F).
The order/cluster of the initials is as follows:
bo po mo fo - labial - pronounced using lips
de te ne le - alveolar - pronounced with tongue touching the alveolar ridge right behind upper front teeth, just like in English d, t, n, l
ge ke he - velar - pronounced with back part of tongue against back part of roof of mouth, just like in English g, k, h
ji qi xi - alveolo-palatal - pronounced with the tip of tongue low, touching bottom teeth for example, while rest of tongue curved upwards towards roof of mouth
zhi chi shi ri - retroflex - tongue tip curved up and back, like pronouncing English r, and while holding that tongue position static, pronouncing English "jer", "chur", "sure", "rur" for zhi chi shi ri respectively
zi ci si - alveolar like de te ne le above - tongue tip on alveolar ridge and pronounced English "ts" for zi ci, and English "suh" for si
So these initial consonant clusters involve the same basic tongue/mouth positions, and within the clusters are smaller differences in pronunciation like nasal, aspiration, etc. Once you understand the positions and watch the kids videos a bunch of times, you assimilate the phonetics very well. There are only 5 basic mouth/tongue positions that cover all the initial consonants, and these positions are used in English as well. The only real challenging ones are ji qi xi, the alveolo-palatals, but apparently they're also used in Russian and other Slavic languages:
https://en.wikipedia.org/wiki/Alveolo-palatal_consonant
This is a good Pinyin alphabet song:
https://www.youtube.com/watch?v=b9Ayvjy-Dgs
There are also Pinyin alphabet songs in the tune of the English ABCs song, which may be easier:
https://www.youtube.com/watch?v=EReU1BKtAXo
Korean has the hardest phonology of the 3 East Asian languages Mandarin, Japanese, and Korean. It also has the worst Romanization. Japanese phonology is easiest, with only 3 basic vowels, similar to Spanish.
Also, despite the simple alphabet, I find Korean hard to read because like Japanese much of its vocab comes from Chinese, and is often the identical Chinese word in Chinese and Japanese, just pronounced in the Korean way. But when written in the Korean alphabet it can be vague because there are so many homonyms without the visual meaning of the Chinese character and no tones hence tone marks in Korean.
One good thing though is that the pronunciation changes for the Chinese character word used in Mandarin, Korean, and Japanese are fairly regular. So if you know how a Chinese character word is pronounced in one of the 3 languages, you generally know how it will usually sound in the other 2.
I think Korean would be best written in "mixed script" similar to how Japanese is written and how it was in the last century. Korean mixed script is even better than Japanese mixed script because Korean mixed script is strictly regular: only Chinese character derived words are written in Chinese, while Korean words and Korean grammatical words are written in hangul, while in Japanese Kanji is used for both Chinese and Japanese words and pronounced in either Chinese style or Japanese depending on use and context.
https://en.wikipedia.org/wiki/Korean_mixed_script#Examples