See the rulings for this card on Gatherer: Gatherer: Nightveil Spectre
- The card is exiled face up. All players may look at it.
- Playing a card exiled with Nightveil Spectre follows all the normal rules for playing that card. You must pay its costs, and you must
follow all timing restrictions, for example.
- Nightveil Spectre’s last ability applies to cards exiled with that specific Nightveil Spectre, not any other creature named Nightveil Specter. You should keep cards exiled by different Nightveil Spectres separate.
The cards are effectively put to one side, to be used as you see fit. It's as if they are added to your hand. You can play them when you choose, but you have to follow the usual rules for playing those cards, including costs and timings. So you're still restricted to playing one land per turn.
The order of exile isn't relevant here, only the copy of the Spectre that exiled the card. So if it was exiled last turn it’s still available to you. This is because exile is effectively a place, the card has been removed from the game, and it stays that way until something changes its state… like you choosing to play it.