The rules for delve have changed slightly since it was last in an expansion. Previously, delve reduced the cost to cast a spell. Under the current rules, you exile cards from your graveyard at the same time you pay the spell's cost. Exiling a card this way is simply another way to pay that cost.

Delve doesn't change a spell's mana cost or converted mana cost. For example, Dead Drop's converted mana cost is 10 even if you exiled three cards to cast it.

You can't exile cards to pay for the colored mana requirements of a spell with delve.

You can't exile more cards than the generic mana requirement of a spell with delve. For example, you can't exile more than nine cards from your graveyard to cast Dead Drop.

Because delve isn't an alternative cost, it can be used in conjunction with alternative costs.