While you control Into the Pit, you can look at the top card of your library whenever you want (with one restriction; see below), even if you don't have priority. This action doesn't use the stack. Knowing what that card is becomes part of the information you have access to, just like you can look at the cards in your hand.

While you control Into the Pit, if the top card of your library has disguise or morph, you may cast it face down from the top of your library by paying and sacrificing a nonland permanent.

You pay all costs and follow all timing rules for spells cast from the top of your library this way.

If the top card of your library changes while you're casting a spell, playing a land, activating an ability, or taking a special action, you can't look at the new top card until you finish doing so. This means that if you cast a spell from the top of your library, you can't look at the next one until you're done paying for that spell.