Why does it seem like every other jazz standard is written by Antonio Carlos Jobim? Because he was a stinkin' genius. He combined interesting rhythms, beautiful melodies, luscious harmonies and cerebral lyrics. A perfect example of all these elements in Triste. This song should be in every player's bag of tricks.
Like most Jobim songs, Triste takes an excursion through various key centers, but does it so elegantly that the player can easily be tricked into thinking this is simple harmonically. It isn't. You really have to learn the melody and the chords internally. Nearly half the chords are part of a ii-V pattern. Whenever you see a ii-V pattern, you can consider it to be a single chord, so the chord changes don't come as quickly at may appear at first glance.
The song form is a straightforward 32-bar ABAB, except that bars 31 & 32 are usually repeated, making a 4-bar vamp, or a total chorus of 34 bars.