The player to your left reveals cards from his deck until revealing an Action card, then discards the rest. You may play that card. When that player's card leaves play, put it into his discard pile or on top of his deck, his choice.
This allows you to play an Action card from your neighbor's deck. You do not keep their card past the end of your turn. It is always returned to its original owner, who decides whether it will go on top of their deck or discard pile.
When the player reveals an Action from their deck, you may decide that you do not want to play it, which ends the action. You may not keep looking for an Action that you want beyond that first revealed one.
If, after revealing all cards from the player's deck - including shuffling their discard into a new deck if need be - no Action is revealed, then Conscription does nothing.
In any case, all other revealed cards are placed into that player's discard pile.
The conscripted card is treated as being yours until the end of your turn - unless it would be trashed, put into your deck, discard, play mat or any other area. In these cases, the card is set aside and returns to its owner at the end of your Clean up phase.
When you play the card or set it aside, place the card in a way to indicate that it belongs to its original owner, so you don't lose track of who it belongs to.
If multiple cards are conscripted on the same turn, you decide in what order their owner resolves putting them back into their deck or discard.
This is not an Attack card.