If you get a wind shift, or your helmsman changes course suddenly, or if you just neglect it for a moment, your selfish spinnaker will collapse. Unfortunately, the spinnaker doesn't luff gently when it collapses; it flaps in a loud manner that makes you feel like something is very wrong.
The key to a calm and successful takedown is to plan it early enough that the helmsman can keep the boat pointing downwind hiding the lowered spinnaker behind the mainsail until everything is cleaned up. Here are the steps to a cruising takedown:
Turn the boat onto a very broad reach and hoist the jib.
Collapse the spinnaker by easing the guy forward and pulling in the sheet. The sail collapses and is docile, protected from the wind behind the mainsail.
Grab the sheet and begin pulling the sail on board.
Ease the halyard in concert with the sail being pulled in so it doesn't fall into the water (drops too fast) or require a struggle by the takedown team (drops too slow).
Stuff the spinnaker into the forward hatch (if you have one) or into the back hatch or spinnaker bag on a smaller boat.
Lower the pole and secure it and the spinnaker sheets.
When Peter raced in the America's Cup, his team had four different varieties of takedowns. Dinghies and smaller keelboats often take the spinnaker down on the windward side in races. You can also find several other types of racing spinnaker sets. But those methods all require tons of practice, whereas the good ol' cruising set and takedown work on any boat and are the easiest way to get that colorful sail up and down.