Pushing is a Learned Skill
Sure, it looks easy enough in the movies -- and in that scary Lamaze video you watched. But pushing a baby through your birth canal and out what seems a logistically impossible opening is probably not going to come naturally. Not only will you need a few practice pushes, but you should be prepared to receive some impromptu instruction from a well-meaning attendant.
Unfortunately, this advice (though a helpful visual aid) is likely to stick with you for years, just like a song that you can't get out of your head -- something along the lines of bearing down and how similar the action is to a bowel movement. Which, by the way, is also likely to happen while you're pushing. Before you freak out about evacuating your bowels in front of complete strangers (which might actually be preferable to doing so in front of your mother-in-law), don't worry: Those people in the room wearing the professional-looking scrubs? This isn't their first rodeo. Not only will they not react, they'll simply whisk the poo into a nearby receptacle. And you? There's so much going on down there, you won't even know it happened.