Nothing fancy, really. You press and hold the Skip Button, and the game fast forwards to the end of a cutscene. Skipping is possible after you watched that whole cutscene once.
Keep in mind that the countdown will fast forward as well. So, no, you won't be able to cheese it by skipping the long-winded cutscenes specially designed to waste your precious in-game time. Unless you use some very obscure tricks.
Also, the characters know when you skip. So there's a chance they may troll you in some way. Keep your attention sharp!