There are two different types of enemies that can be spawned:
The procedure for spawning On Deck enemies is to determine how many spawn points will be used (the effect that triggers the spawning will say how many points to use; often it is equal to the current Act), and turn up Enemy Cards from the Enemy Deck, one at a time, until the value of all the Act numbers on the Enemy Cards are equal to the number of spawn points to use. If you turn up an Enemy Card that would make total higher than the number of spawn points, discard that card and draw a new one until the values match. Then place the miniatures corresponding to the drawn Enemy Cards on an unoccupied blank (black) Node in the On Deck area of the appropriate Ship Board.
If the Enemy Card tells you to spawn a specific type of enemy, but all miniatures for that enemy are already in play, skip placing the enemy and instead advance the Enemy Agenda as if the enemy had been Banished.
The procedure for spawning Enemy Ships is to draw one Enemy Card for the ship, determine the destination for the ship based on the instruction in the lower right on the Enemy Card, and then place an enemy ship miniature on the Game Board in the hex where it spawns, turned so it faces toward it destination.
If the criteria for selecting the destination can't be fulfilled, for example if the ship's destination is an island but no island has yet been revealed, the ship spawns without having a destination and only aims to attack players until something that fulfills the destination criteria shows up. (This was an answer from the game designed posted on BoardGameGeek; his exact answer was "In this case, yes, the enemy ship would not move until a player ship enters its Engagement range, or an island is revealed. This actually feels quite sinister, like the enemy ship is guarding that area waiting to strike!")