Casting a foretold card from exile follows the timing rules for that card. If you foretell Green Slime (or an instant card), you can cast it as soon as the next player's turn. In most cases, if you foretell a card that isn't an instant (or doesn't have flash), you'll have to wait until your next turn to cast it.

Because exiling a card with foretell from your hand is a special action, you can do so any time you have priority during your turn, including in response to spells and abilities. Once you announce you're taking the action, no other player can respond by trying to remove the card from your hand.

If you're casting a foretold card from exile for its foretell cost, you can't choose to cast it for any other alternative costs. You can, however, pay additional costs, such as kicker costs. If the card has any mandatory additional costs, those must be paid to cast the spell.

Triggered abilities use the word “when,” “whenever,” or “at.” They're often written as “[Trigger condition], [effect].”

Mana abilities don't use the stack and can't be responded to, so they cannot be countered this way.

Activated abilities contain a colon. They're generally written “[Cost]: [Effect].” Some keywords are activated abilities and will have colons in their reminder text.