The rules say : "When placed from anywhere to your Discards. The effect continues while the card in your Discards."
The Trash mechanics is indeed not clear.
It seems that instead of playing one of your cards (2nd step of the Sequence of play), you can trash a card present in the play area, probably only the ones on the other players' discard piles as these are the only ones face up.
If so, the sequence of play should have been clarified. I wonder if you can trash a card that you've just looked at (Scout).
I'm thinking that Trash is not a new mechanic, just a short-hand way to say "when this card is in your discard area", since I believe some of the other cards let you steal other player's discards.