Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Cynical, Bitter
If this play were a person, we'd tell you it has a lot of mood swings. One minute Shakespeare's cracking (mostly dirty) jokes and the next minute, the play is all doom and gloom. Ultimately, though, Troilus and Cressida is cynical and bitter, especially about the subjects of warfare and love, which are both portrayed as treacherous and futile. (We talk about this more in "Themes.")
So, if you want to survive this play, you might want to think about growing a thick skin ASAP. Things gets pretty bloody when the Trojans and Greeks hack into each other on the battlefield. Plus, there's a ton of disease in this play, most of which is sexually transmitted. In fact, a dying Pandarus stands alone on stage at the end and says he really hopes we all get syphilis and die.
No wonder Joyce Carol Oates says that "no darker commentary on the predicament of man has ever been written" (source).