Most instructions must be followed immediately. For example, if you are instructed to move or to destroy a minion, you must do so when instructed. "Play an extra minion" and "play an extra action" are special. The instruction simply raises the limit on the number of minions or actions you can play this turn. (Rule quoted at the bottom.)
For example, Insta-Grow (Action from the Plants) reads
Play an extra minion.
You may play one more minion than you otherwise could this turn.
Before playing Insta-Grow, you can play up to one Action and one Minion on your turn.
After playing Insta-Grow, you can play up to one Action and two Minions on your turn.
Minions and Actions can be played in any order — they can even be intermixed — and you need not play all the cards you can play.
Extra: Normally, you can play one minion and one action each turn. A card that lets you play an extra minion or action lets you play an additional card of that type during that turn. You don't have to play the extra card right away unless the extra card was gained by a Special ability.
[Accompanying example of "Extra" is "Spreading the Word". Action: Play up to two extra minions with the same name as a minion in play.]
("Unless the extra card was gained by a Special ability" wasn't present in the original game's rules. This quote comes the Cthulhu set.)