I am coming from playing more typical tabletop. D&D and Pathfinder, things of that nature. In that case, you never really come out and tell the PCs of their objective to receive a certain result.

I am wondering in Quests, do you come right out and tell them the special circumstances in the quest that are affecting them? Like if the Overlord units do this, you lose, if you do this, you win.

Or do you leave it vague and for them to figure out what th eobjective is just from the intro text and perhaps some flavor text thrown in?

I am curious because we were doing the quest "What's Mine is Mine" and the intro wasn't quite specific enough I suppose and my players were wondering what the hell they were supposed to be doing. Clearly they have to kill the named Ettin to win, but the intro quest doesn't mention that I believe. They also don't know why I am collecting ore, or that I can win by collecting enough and leaving.

I am just curious how other Overlords handle those kind of things and what you come right out and tell the players.

All information is public and none should be hidden.

See quest guide, p. 2 "Public information" :

Descent is not a RPG and the OL is not a GM.

It is a tactical skirmish game set in a fantasy environement and the OL is a ruthless opponent of the heroes.

Keeping information away from the latter would give the OL a tactical advantage.

More than just outright telling them the objective, the hero players are free to look at the quest guide whenever they want. They can read the objective for themselves.