In Avatar: The Last Airbender, the underlying language is Classical Chinese. The characters are Chinese used in the Classical Chinese format. The Chinese language format evolved and changed over a long period of time, and Classical Chinese format is very different from contemporary and spoken format. Nowadays Classical Chinese is rarely used (and only in literature) and considered as a proper form to Chinese, just as the Latin or Shakespearean language is to the West.

Classical Chinese is primarily a writing form. It is very hard to learn and understand because it is a very condensed form -- it uses the fewest possible characters to express very comprehensive meanings, and the specific meaning is almost entirely dependent on the context. That is because in ancient China, paper and writing equipment were expensive and rare so people had to be economical with the language.

At the top of the poster, from Left to Right:

#1 = pronunciation: "qing" -- celebrate
#2 = "zhu" -- to wish, to express good wishes

#1 + #2 = just "celebrate" (the common usage in contemporary Chinese is to use the both characters)

#3 = "lie" -- intense
#4 = "huo" -- fire

#3 + #4 = "Fire" as in Fire Nation, Fire Lord, Fire Bending, Fire Army

# 5 = "jie" -- festival

First line near the bottom of the poster:

#1 = pronunciation: "chuan" -- meaning: to pass on, to spread, to transmit, to infect, to transfer, to circulate
#2 = "tong" -- to gather, to unite, to unify, whole

#1 + #2 = (something to be) to passed on/down in order to unite/unify (a people/culture) = tradition

#3 = "lie" -- intense
#4 = "huo" -- fire
#5 = "guo" -- country, state, nation

#3 + #4 + #5 = Fire Nation

#6 = "mei" -- beautiful
#7 = "wei" -- taste

#6 + #7 = beautiful in taste = tasty, delicious

#8 = "shi" -- eat, food
#9 = "pin3" -- thing, product, good

#8 + #9 = food product = foods #6 + #7 + #8 + #9 = delicious foods = delicacies

An interesting note:

#6 = "mei" -- beautiful
#5 = "guo" -- country, state, nation

#6 + #5 = "beautiful nation" = USA! That's the Chinese word for the USA.

1: Wanted:
2: The Avatar
3: This fugitive knows airbending,
4: can create whirlwinds and flee like the wind.
5: Hunters be extremely cautious!
6: By the decree of the Fire Lord.

Line 1 - Left to Right:

1st character, simply pronounced in Mandarin as "G" or "gi" (as in Gigi,) means adhere, capture, or restrain. (I'm not sure about the pronunciation of this particular character.)

2nd characer, pronounced "Na", means: to hold, to seize, to catch, to apprehend, to take.

These two characters are very commonly used together to mean "Wanted." They are commonly used as the title for a warrant or wanted poster, and usually comes with a reward or a bounty.

Line 2 - Left to Right:

#1 = "jiang" -- to drop, to fall, to come down, to descend.
#2 = "shi" -- world, generation, era, lifetime.
#3 = "sheng" -- deity, divine essence, or spiritual being; or, as adjective, it means supernatural, divine, magical, or mysterious.
#4 = "tong" -- to go through, to know well, to connect, to communicate, to serve as a medium. In this context, it is a noun and means "medium" (between the mortal and the spiritual/elemental worlds.)

Together, the four characters combine to mean "the divine medium that has descended onto the mortal world," implying that he/she is a spiritual being reborn as a mortal. So, it means the Avatar.

Line 3:

#1 = "gai" -- meaning: this.
#2 = "tao" -- to escape, to run away, to flee.
#3 = "fan" -- (verb) to violate, to offend; (noun) criminal, felon.

#2 + #3 = escaped criminal = fugitive

#4 = "shen" -- body (of a person or animal)
#5 = "huai" -- to carry (with both hands)

#4 + #5 = to be carried by/with body = to possess, to know

#6 = "jie" -- to cut off, to bend.
#7 = "qi" -- air.
#8 = "shen" -- magical, mysterious, spiritual, divine, holy.
#9 = "gong" of "kong" as in "kong fu" -- art, skill, ability.

#6 + #7 + #8 + #9 = the magical art of bending air = airbending

Line 4:

#1 = "neng" -- meanings: can, may, capable, able
#2 = "zhi" -- to create, to make.
#3 = "qi" -- to rise, to raise.

2nd + 3rd characters = to create out of thin air

#4 = "xuan" -- to revolve.
#5 = "feng" -- wind.

4th + 5th characters = wind that revolves itself, revolving wind = whirlwind, tornado

#6 = "fei" -- to fly.
#7 = "dun" -- to disappear, to escape.

#8 = "ru" -- like, as if.
#9 = "feng" -- wind.

Line 5:

#1 = "bu" -- to repair, to mend, to fill (a vacancy), to capture
#2 = "zhen" -- a person who does something.

#1 + #2 = person who captures = hunter, in here it means bounty hunter or government/official hunter (i.e., a police)

#3 = "shen" -- cautious
#4 = "zhi" -- of, in this context, means beyond
#5 = "shen" -- cautious

#3 + #4 + #5 = be cautious beyond cautious = be extra/extremely cautious

6th "character" is not really a character -- it is a punctuation to end a paragraph, like a full stop or exclamation mark.

Line 6:

#1 = "lie" -- intense, forceful.
#2 = "huo" -- fire

(#1 + #2 just mean "Fire" as in the Fire Nation, the Fire Lord, the Fire Army.)

#3 = "jun" -- monarch, lord, ruler
#4 = "ling" -- to order, to command, to decree

A: Wanted:
B: Jeong Jeong
C: Former Fire Nation Admiral
D: Age Sixty
E: White Haired
F: Appears Gentle
G: In Truth Skilled in Firebending
H: Bounty Hunter Be Cautious

This poster includes 8 separate sentences, A to H.

sentence A (2 characters) = Wanted (see past translation for the "Wanted: Avatar" poster)

sentence B (2 characters) = Jeong Jeong (pronunciation is the same; as is the two characters)

sentence C (6 characters):

#1 = "qian" -- before, in front, ago, former, previous

#2 + #3 + #4 = Fire Nation (see past translation for the "Traditional Fire Nation's Delicacies" poster.)

#5 = "jian" -- warship
#6 = "zhang" -- chief, head, elder

#5 + #6 = head of warship or war fleet = admiral (the two characters do not mean ship captain; another character combination are used to refer to captain: "head of ship")

sentence D (3 characters):

#1 = "nian" -- year, age
#2 = "liu" -- six
#3 = "shi" -- ten

#2 + #3 = six of ten, six tens = sixty

sentence E (2 characters):

#1 = "bai" -- white
#2 = "fa" -- hair

sentence F (4 character):

#1 = "mao" -- appearance
#2 = "si" -- to seem, to appear, similar, like, to resemble

#1 + #2 = appearance seems as = appear

#3 = "rou" -- soft
#4 = "shun" -- to obey, to follow

#3 + #4 = soft and obedient = gentle, cooperative

sentence G (5 characters):

#1 = "shi" -- real, true, honest, really
#2 = "chang" -- (is) skilled in
note: this is the same character as "zhang", meaning chief, head, elder (see sentence C character #6); it has a different pronunciation and meaning when used in this different context.

#3 = "zhi" -- to make, to manufacture, to control
#4 = "huo" -- fire
#5 = "shu" -- method, technique

#3 + #4 + #5 = method to make/control fire = firebending

sentence H (4 characters):

#1 + #2 = Bounty Hunter (see past translation for the "Wanted: Avatar" poster.)
#3 = "shen" -- cautious
#4 = "zhi" -- of

Wanted:
Blue Spirit.
[did something to] the Avatar.
Head worn blue color [mask?] [blah blah blah].
[blah blah blah blah]
If [blah blah] (then) must [blah blah]

Here are the only characters I can barely read:

#1 + #2 = Wanted (again, see translation for the "Wanted: Avatar" poster)

#3 = "lan" -- blue
#4 = "shen" -- spirit

#5 = "shi" -- world, generation, era, lifetime
#6 = "shen" -- deity, divine essence, or spiritual being; or, as adjective, it means supernatural, divine, magical, or mysterious.
#7 = "tong" -- to go through, to know well, to connect, to communicate, to serve as a medium. In this context, it is a noun and means "medium" (between the mortal and the spiritual/elemental worlds.)

so, the character before #5 + #5 + #6 + #7 = "the divine medium that has descended onto the mortal world" = The Avatar So, although I can't read two characters in the first right vertical line, I assume the line/sentence means "Blue Spirit. Rescued(?) The Avatar."

#8 = "tou" -- head
#9 = "dai" -- to put on, to bear, to wear
#10 = "lan" -- blue
#11 = "se" -- color

So, the first few characters in the second line from the right means "Head worn blue color (mask?)"

#12 = "ru" -- if (note: I'm not sure; it's too blurry.)
#13 = "xu" -- must (again, I'm not sure.)

So, the leftmost line probably means "if (anyone sees him or whatever, then one) must (do something)." I'm just making a wild guess based on the only two characters I can barely recognize from the line. All the other characters are just too fuzzy for me to make out.