When exactly can you ambush a card?

Does it stay on the table? or attached?

You can play a card with the Ambush keyword any time you could play an "Any Phase:" action.

As for the second part, I don't really understand the question. The card stays in play (on the table), and attachet, if it was an attachment.

Not to put words in anyone's mouth, but I think the second part was kind of asking "Since Ambush cards play kind of like events, do they go to the discard pile immediately the way that events do?"

The thing to keep in mind that Ambush is a "put into play" effect. So you are not "playing" the card when you use Ambush - you are putting it into play. Since you are "putting it into play" (and doesn't have any specific "discard at the end of the phase" or the like associated with it), it does, indeed, stay in play until some other effect removes it from play.