when nightveil spector exiles the top card of opponents library i can play it....do i have to pay for it or not???
Yes, you do have to pay for them. It would have to specify "without paying their mana cost" in order to play them for free.
The good news is that {Nightveil Specter} says you can play the cards, not cast - this means you can use lands of your opponent't that you've exiled to pick up those extra colors in costs that your deck doesn't have.