How do you say, "say goodbye," in Latin?

Answer 1

To one person

Vale! (A command) literally "Be Strong"

Valete (2+)

avē atque valē (avete atque valete)

is more formal (Hail and Be Strong) As seen in a poem by the poet Catullus in a grief struck poem to his deceased brother:

http://blogs.dickinson.edu/catullus/tag/catullus-101/