So, when going into a broad reach, I would still leave my Spinnaker at a beam reach position?
When you say "it comes down before you start to sail upwind" Does that mean that it gets "put away?"
Is there a fast and easy way to "put it away?"
The spinnaker is only tied onto the boat in 3 positions. It's a roughly triangular symmetrical sail. The halyard holds it up, and the sheets trim it in. However, a spinnaker pole is used as well. This pole is placed on the windward side of the boat and is attached to the windward sheet.
As you turn the boat further downwind, you would ease out the jib and mainsail. However, you would shift the spinnaker around the front of the boat towards the wind so you can catch more wind. If you let the spinnaker out as you went downwind, it would go behind the jib and mainsail and not fill.
There's way more complex things to do with the spinnaker, but don't worry about them quite yet.