The arm sits outside the brackets, raised on one side. The most common arm is ノ, a half width Japanese letter "no". Its slant looks like a hand in the air.
The parts of (☞゚∀゚)☞
☞U+261EWhite right pointing index. The pointing hand.
゚U+FF9FHalf width katakana sound mark. A small round eye.
∀U+2200For all, a sign from logic. The open mouth.
The pointing hand ☞ is older than computers. Readers drew it in the margins of old books to mark an important line, and printers later cast it as type. It is called a manicule. ∀ is a math sign that means "for all". Upside down, it makes a wide open mouth.
ヾ is a Japanese mark that means "repeat the last sound, but voiced". In a face it is just a hand waving next to the head.
Faces for two people
Some faces need two heads. In ('_')┏oo┓('_') the two o letters are fists meeting in the middle. In ♪ヽ( ⌒o⌒)人(⌒-⌒ )v ♪ the Chinese character 人, which means "person", looks like two hands slapping a high five.
Good morning and good night
A stretch with both arms up says good morning. A face with closed eyes and the words written in tiny raised letters says good night.
For more sleeping faces, see the activity faces. The small letters in "gᵒᵒᒄ ᵑⁱgᑋᵗ" come from phonetic alphabets, and ᒄ and ᑋ are letters from Canadian Aboriginal syllabics. That is why some phones show a box in place of a letter.
Type a face like (^_^) and add a slanted line for the arm: (^_^)/ or \(^_^). For the Japanese ノ arm, copy it from this page, since most keyboards don't have it.
What does (☞゚∀゚)☞ mean?
It points at the other person with both hands and a big grin. People use it to say "you, my friend!" or "nice one".
Can I add my own name to a face?
Yes. Use the "Wave and add a name" box above. Pick a face and a greeting, type a name, and click the result to copy it.
Why does part of a face show a box?
Your phone or app has no font with that one character. The face is still fine. It shows correctly on devices that have the character.