Each letter has a name, of course, but I was told by one of my Korean teachers that when people say the alphabet, they don't say the name, they just make the sound of each consonant, followed by an "a" sound. So it goes ga, na, da, ra, ma, and so on. The way most of the letters are named is cool, though, and easy to remember. You simply start with the sound of the consonant, add the "ㅣ" (long "e") sound, then add the "ㅡ" ("eu") sound, then end with the sound of the consonant again. A few of the letters don't follow that rule, due to certain restrictions coming from Chinese at the time of Hangeul's invention. North Korea actually went on to regularize those letter names, but South Korea never did.
Alphabetical order is called "ganada" order, "ga," "na," and "da" being the first three sounds made when saying the alphabet. Compare to "ABC order" or even "alphabetagamma order." The actual order seems to be somewhat variable. According to Wikipedia.org, the order I am about to present the letters in is the current South Korean standard. In my Korean textbook, however, the index is presented with the "double" letters at the end. North Korea uses the latter order, except with the distinction between the two functions of the letter "ieung," which I will discuss below. Vowels are not mixed in with the consonants. They are usually placed at the end, I believe. When using the order to organize words, as in a dictionary, in the case of "ieung" appearing only once in the alphabet, the words beginning with a vowel are placed within that letter's listing (again, see below).
Here are the letters and some info about each one:
ㄱ
giyeok (기역)
This letter makes a sound that is between a "g" and a "k." It is not aspirated. The symbol represents the back of the tongue rising up to touch the back of the palate on the roof of the mouth.
ㄲ
ssanggiyeok (쌍기역)
This letter makes a really hard "g" sound. "Ssang" means "twin" or "double."
ㄴ
nieun (니은)
This letter makes an "n" sound. The symbol shows the tip of the tongue rising up to touch the ridge behind the teeth.
ㄷ
digeut (디귿)
This letter makes a sound that is between a "d" and a "t." It is not aspirated. The symbol represents the same tongue shape as with "ㄴ" but the top line indicates firm contact with the roof of the mouth.
ㄸ
ssangdigeut (쌍디귿)
When I was learning how to read Hangeul back in LA, my teacher told us that this letter makes a really hard "d" sound, but Rosetta Stone seems to pronounce it more like a hard "t." I guess either it varies by speaker, or my ear isn't enough in tune yet to understand what I'm hearing.
ㄹ
rieul (리을)
This letter makes a sound that is between an "l" and an "r," and is where we get the confusion with, for example,"rice" and "lice." It is formed by tapping the tongue at the center of the roof of the mouth, as opposed to touching it to the gum ridge for "l" or lowering and curling it for "r." In lingustistics, this action is called a "flap" (and so is the letter). This is a very hard sound to make, and evidently a very hard sound to leave behind when learning Western languages. The symbol represents the same tongue formation as "ㄴ," with the rop representing the flap.
ㅁ
mieum (미음)
This letter makes an "m" sound. The symbols shows the lips coming together to make the sound (a little abstract).
ㅂ
bieup (비읍)
This sound makes a sound between a "b" and a "p." I like to think of it as the alien head letter. It is not aspirated. The symbol represents the shape of the mouth, as in "ㅁ," but the extended vertical lines indicate the sound bursting from the mouth.
ㅃ
ssangbieup (쌍비읍)
This letter makes a hard "b" sound.
ㅅ
siot (시옷)
This letter makes a soft "s" sound, like in "snow." The symbol represents a side view of the (bottom) teeth. I'm not sure why it's drawn this way, since that sound has nothing to do with those teeth. I'd like to officially theorize that Sejong meant the line on the right to represent the tongue rising up to the gum ridge, and the line on the left to indicate the front of the gum ridge descending toward the upper teeth.
ㅆ
ssangsiot (쌍시옷)
This letter makes a hard "s" sound, as in "song."
ㅇ
ieung (이응)
This letter has two functions (yes, now we come to it). The consonantic function is that of the "ng" sound. It is more commonly used, however, as a "null" letter, to be placed in front of syllables the want to begin with a vowel. As I said in the Vowels entry, no syllable can actually begin with a vowel (I don't know why). So this silent consonant is placed before the beginning vowel to make it legitimate. The symbol shows the shape of the throat, which is near where the "ng" sound is made.
ㅈ
jieut (지읒)
This letter makes a "j" or "dge" sound. The shape comes from the shape of "ㅅ," with the top line indicating firm contact of the tongue tip with the gum ridge.
ㅉ
ssangjieut (쌍지읒)
This letter makes a hard "dge" sound.
ㅊ
chieut (치읓)
This letter makes a "ch" sound. The shape is derived from "ㅈ," with the small top line indicating aspiration.
ㅋ
kieuk (키읔)
This letter is much closer to our actual "k" sound. In English, "k" is aspirated, which is what makes it different from "g." Kieuk and giyeok have a similar distinction, The shape of "ㅋ" comes from "ㄱ," with the lower horizontal line representing that aspiration.
ㅌ
tieut (티읕)
This letter is the aspirated form of "ㄷ," which is what the middle line represents. Again, this letter is more like our "t" than "ㄷ" is, because our "t" is aspirated.
ㅍ
pieup (피읖)
Another aspirated letter, this one is much like our "p." It comes from "ㅂ," although the shape got a bit mangled in the process of adding that extra top stroke for aspiration. Maybe someone had one too many soju shots.
ㅎ
hieut (히읗)
This letter makes an "h" sound. It comes from "ㅇ." The top line represents the aspiration, and the middle line is from an obsolete letter, which was a glottal stop. A glottal stop is a cutting off of sound, like at the end of the first syllable in "uh-oh."
I did not include the Romanization of the consonants like I did with the vowels, but I'm going to have an entry explaining that process with both letters and words soon, so you'll see how that goes.