The creature card with augment isn’t put onto the battlefield until the ability resolves. This means if the host is destroyed, the creature with augment stays in your hand. You can’t choose a different host, but you can activate augment again if there’s another host available.

Creatures with augment don’t have a mana cost and can’t be cast.

Augment can’t target creatures that aren’t host creatures.

You can’t activate augment unless there is a host creature on the battlefield. It doesn’t need to be yours. Note though that if you augment another player’s host creature, they control the combined creature.

Augment can (and usually does) change the name, card types, subtypes, rules text, and power/toughness. The combined creature will have (at least) two artists and may now have multiple colors. Anything covered up in the augment process doesn’t count, so ignore things to the left of the “metal bar” in the art of host creatures.

You can’t put more than one augment card on a single host creature. Once a host creature is augmented, the host part gets covered up and it’s no longer a host creature.

Augment is an activated ability that you activate from your hand. To do so, reveal the card, choose a target host creature, and pay the augment cost. As this ability resolves, if the card with augment is still in your hand, put it onto the battlefield combined with the host creature.